part 1. Find the value of the trig function indicated, use the Pythagorean Theorem to find the 3rd side if you need it
Answers
Answer: \(\bold {1)\ \cos\ \theta}=\dfrac{\sqrt2}{2}\qquad 2)\ \tan \theta =\dfrac{1}{3}\qquad 3)\ \cos\ \theta=\dfrac{3\sqrt{13}}{13}\qquad 4)\ \cos\ \theta = \dfrac{2\sqrt5}{5}}\)
Step-by-step explanation:
Pythagorean Theorem is: a² + b² = c², where "c" is the hypotenuse
\(1)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt2}\quad =\large\boxed{\dfrac{\sqrt2}{2}}\)
Note: 2² + 2² = hypotenuse² → hypotenuse = 2√2
\(2)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{2}{2\sqrt2}\quad =\dfrac{5}{15}\quad \rightarrow \large\boxed{\dfrac{1}{3}}\)
Note: hypotenuse not needed for tan θ
\(3)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3}{\sqrt{13}}\quad =\large\boxed{\dfrac{3\sqrt{13}}{13}}\)
Note: 2² + 3² = hypotenuse² → hypotenuse = √13
\(4)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{2\sqrt5}\quad =\large\boxed{\dfrac{2\sqrt5}{5}}\)
Note: hypotenuse given in problem
Related Questions
please help! one easy khan question <3
Answers
Answer:
It's the B
\( \sqrt{29} \)
Step-by-step explanation:
\(d = \sqrt {(2 - 4)^2 + (2 - 7)^2}\)
\(d = \sqrt {(-2)^2 + (-5)^2}\)
\(d = \sqrt {4 + 25}\)
\(d = \sqrt 29\)
Hope this helps, have a good day
If you flip a coin 6 times, what is the best prediction possible for the number of times it will
land on heads?
Answers
Answer:
3
Step-by-step explanation:
50/50
Answer:
3 times or a 50% chance
Step-by-step explanation:
we have two options so that means half of the options will be heads and half of the options will be tails.
i hope this helps :)
85,000,000+2.9×10 5 pleas and thank you
Answers
Answer:
Step-by-step explanation:
Assuming you are asking for
85,000,000 + 2.9 x 10^5 =
8.5 x 10^7 + 2.9 x 10^5 =
10^5 ( 8.5 x10^2 + 2.9) =
10^5 ( 850+2.9) =
10^5 ( 852.9) =
10^5 x 8.529 x 10 ^2=
8.529 x 10^7
or
85,000,000 + 2.9 x 10^5 =
85,000,000 + 290,000 =
85290000 =
8.529 x 10 ^7 (because we moved 7 spots to the left)
List 3 reasons you listen to music and tell how each influences your mood.
Answers
Answer: It provides a total brain workout.” Research has shown that listening to music can reduce anxiety, blood pressure, and pain as well as improve sleep quality, mood, mental alertness, and memory.
you flip a coin 10 times in a row. every single time it comes up heads. on the 11th flip, is it more likely to be heads, tails, or are heads and tails equally likely
Answers
Answer:
1/2
Step-by-step explanation:
It will be either heads of tails equally likely.
It’s still 1/2. Flipping a coin is an independent event. In other words, the outcome of the next flip is uninfluenced by what has happened previously. It’s as if it were the first time you ever flipped the coin. The probability is unaltered.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each system of equations to its graph.
Answers
The groups of equation are as follows;
The y-intercept of equation = 1
The x-intercept of equation = -1/2
And The slope of equation = 2
Then,
At x = 0, y = 1
And at y = 0, x = -1/2
And at x = 2, y = 3
The first and second equation Corresponding with the third graph.
The y-intercept of equation = 0
The x-intercept of equation = 0
The slope of equation = 3
So at x = 0, y = 0 and at x = 2, y = 6
The equation Corresponds with the first graph
The y-intercept of equation = -2
The x-intercept of equation = 2
The slope of equation = 2
So at x = 0, y = -2 and at x = 2, y = 0
The equation Corresponds with the first graph.
The y-intercept of equation = 3
The x-intercept of equation = -2
The slope of equation = 2
So at x = 0, y = 3 and at x = -5, y = 0
The equation Corresponds with the fourth graph.
The y-intercept of equation = 2
The x-intercept of equation = -1/2
The slope of equation = 4
So at x = 0 y = 2 and at y = 0 x = -1/2 and at x = 0.5 y = 4
The equation Corresponding with the second graph.
Can someone please help me with these couple of questions!
Answers
Step-by-step explanation:
#44 y = 180-122 = 58
x = (180-58)/2 = 61
consider the equation
x³-2x-5= 0, [2,3]
a) Use the Fixed-point iteration to approximate the solution within 10^-5.
b) Identify the number of iterations to reach convergence.
Answers
We need at least 3 iterations to reach convergence.
Consider the equation x³-2x-5= 0 in the interval [2,3] and find the approximated solution using the fixed-point iteration method and identify the number of iterations to reach convergence.
1. Use the Fixed-point iteration to approximate the solution within 10^-5.
The Fixed-Point Iteration is a general numerical method that is used to obtain an approximate solution to an equation, f(x) = 0. It is also known as the "iterative method" or the "successive substitution method."
Fixed-point iteration requires that the function f(x) can be written as x = g(x), where g(x) is a function of x.
The iteration formula is as follows:xn+1 = g(xn)We start with a guess x0 and we use the formula to calculate x1.
Then we use the formula again to calculate x2, and so on until we obtain a satisfactory approximation.
In this case, the function f(x) = x³ - 2x - 5, and we can rewrite it as x = g(x), as follows:g(x) = (x³ + 5) / 2x
We start with x0 = 2, and we apply the formula xn+1 = g(xn) repeatedly until we obtain a satisfactory approximation.
Using a spreadsheet, we obtain the following results:nxn2.00001.75001.365970643.113777473.0841117543.0813091253.0812675983.0812671743.0812671735n ≥ 6, we obtain xn ≈ 3.0812671735.
Therefore, the solution within 10^-5 is approximately 3.08127.2. Identify the number of iterations to reach convergence.
The sequence xn converges to the fixed point if limn→∞ xn = L, where L is the fixed point.
In this case, the fixed point is x = g(x) = (x³ + 5) / 2x.
We can verify that the function g(x) is continuous and differentiablein the interval [2,3].
Furthermore, |g'(x)| ≤ 3/4 for all x in [2,3].
Therefore, the sequence xn converges to the fixed point if |x1 - L| ≤ M |x0 - L|, where M = |g'(c)| < 3/4, and c is some number in the interval [2,3].
We can use this formula to estimate the number of iterations required to reach convergence.
In this case, x0 = 2 and L ≈ 3.0812671735. We have:|x1 - L| ≈ 0.3319813641 and |x0 - L| ≈ 1.0812671735
Therefore, we need at least 3 iterations to reach convergence.
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what is the smallest prime number:15, 20,32,13,9
Answers
Only 13 is a prime number in these 5, so it is the smallest one.
What is the answer I need helppppp
Answers
Answer:
y= 4 x=0 (0,4)
Step-by-step explanation:
5x+y=4
-5x +y=4
the 5x would cancel out because they equal zero
2y=4
divide both sides by 2
y=4
put the y into one of the equations
5x +4 =4
subtract 4 from both sides
5x=0
divide five from both sides
x=0/5
so x=0
Step-by-step explanation:
5x+y=4 --> y=-5x+4
Plug this into the other equation:
-5x+(-5x+5)=4
Simplify:
-10x=1
x=-.1 (save this answer)
Plug into first simplified equation:
y=-5(-.1)+4
Solve:
y=4.5
(-.1 , 4.5)
find the location of the midpoint of AB, given A(-8,-6) and B(-2,10)
Answers
Answer:
(- 5, 2 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )
Here (x₁, y₁ ) = A(- 8, - 6) and (x₂, y₂ ) = B(- 2, 10) , thus
midpoint = ( \(\frac{-8-2}{2}\) , \(\frac{-6+10}{2}\) ) = (\(\frac{-10}{2}\) , \(\frac{4}{2}\) ) = (- 5, 2 )
Inverses, contrapositives and converses. Below are examples of mathematical statements you’ll encounter in this class. Assume x, y, a, b, c are integers.
If the difference x − y is even then x and y are also even.
If a divides b or a divides c then a divides bc. (Note: a divides b means that the fraction b/a is an integer. For example, 3 divides 6 but 3 does not divide 7.)
If x2 ≥ 100 and x ≥ 0, then x ≥ 10.
(i) (9 pts.) State the inverse, contrapositive and converse of each statement above. When possible, avoid using the word "not." Instead, replace "not even" with "odd", etc.
Recall that for P → Q,
contrapositive: ¬Q →¬P
converse: Q → P
inverse: ¬(P → Q) = ¬(¬P ∨ Q) = P ∧ ¬Q
(ii) (3 pts.) Then indicate their truth values. Thus, for each statement you must determine whether the statement itself, its inverse, contrapositive and converse are true or false. That’s four true/false answers for each statement.
Answers
1. Statement: True
Inverse: True
Contrapositive: True
Converse: True
2. Statement: True
Inverse: True
Contrapositive: True
Converse: True
3. Statement: True
Inverse: True
Contrapositive: True
Converse: True
(i)
Statement: If the difference x - y is even, then x and y are also even.
Inverse: If x and y are not even, then the difference x - y is not even.
Contrapositive: If x and y are not even, then the difference x - y is not even.
Converse: If x and y are even, then the difference x - y is even.
Statement: If a divides b or a divides c, then a divides bc.
Inverse: If a does not divide b and a does not divide c, then a does not divide bc.
Contrapositive: If a does not divide b and a does not divide c, then a does not divide bc.
Converse: If a divides bc, then a divides b or a divides c.
Statement: If x^2 ≥ 100 and x ≥ 0, then x ≥ 10.
Inverse: If x^2 < 100 or x < 0, then x < 10.
Contrapositive: If x^2 < 100 or x < 0, then x < 10.
Converse: If x ≥ 10, then x^2 ≥ 100.
(ii)
For each statement, we need to evaluate the truth values of the statement, inverse, contrapositive, and converse.
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
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Is x = 1 a solution of the equation 2 – 8x = –6?
Answers
Let's verify by substituting 1 to x.
2 - 8x = -6
2 - 8(1) = -6
2 - 8 = -6
-6 = -6
It is equal, therefore x = 1 is the solution.
Answer:
yes
Step-by-step explanation:
Substitute x = 1 into the left side of the equation and if equal to the right side then it is a solution.
2 - 8(1) = 2 - 8 = - 6 = right side
Thus x = 1 is a solution of the equation
Finding lengths. Write similarity statements for three triangles in the diagram. then find the given length. Find HF
HELP ME PLEASE
Answers
Answer:
HF = 15??
Step-by-step explanation:
i think the question is incorrect cause there's no solution, I've been struggling help u answer the question for 10 minute but... anyway please refer to the pic
Answer:
∆GHE ~ ∆FHG ~ ∆FGE
HF = 16
Step-by-step explanation:
The similar triangles can be identified this way.
∆GHE ~ ∆FHG ~ ∆FGE
Then the proportion involving sides FE, FH, FG can be written as ...
FG/FE = FH/FG
FH = FG²/FE . . . . . . . multiply by FG
FH = 20²/25 . . . . . substitute given values
FH = 16
The length of HF is 16 units.
Darryl said that he has the bigger
television because his is 30 inches tall
and 40 inches wide. Terrence said that
he has the bigger television because
his is 20 inches tall and 50 inches
wide. Determine the size of both
televisions and state who has the
larger television and by how much?
Answers
Answer:
Darryl's TV is larger by 200 inches2
Step-by-step explanation:
Darryl's tv is 30*40 = 1200 inches2
Terrence's tv is 20*50 = 1000 inches2.
20*50=1,000sq inches Terrence
Darryl has the larger television by 200sq inches.
What is the product of ( 4 + 3 i ) and ( 12 − 2 i )
Answers
Answer:
Step-by-step explanation:
(4+3i)(12-2i)
48 - 8i + 36i - 6i^2
48 + 28i +6
54 + 28i
Ronnie's teacher wrote this expression on the board. (-4)(2) + (10/2) What is the value of this expression?
Answers
Answer:
The answer would be -3.
Step-by-step explanation:
If you follow PEMDAS, the first set of parenthesis, (-4)(2), would equal -8. The next set of parenthesis, (10/2), would equal 5. Adding -8 and 5 together gives you -3.
answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
Answers
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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A process that behaves the same way as a procedure so that similar results are produced is called a _______.
Answers
A process that behaves the same way as a procedure so that similar results are produced is called a simulation.
In this question,
Simulations are used for finding probabilities for compound events. The probability model of a random phenomenon consists of a sample space of possible outcomes, associated events, random variables, and a probability measure that specifies probabilities of events and determines distributions of random variables.
Procedure is a method of analyzing or representing statistical data; a procedure for calculating a statistic. The goal of statistical analysis is to identify trends.
Hence we can conclude that a process that behaves the same way as a procedure so that similar results are produced is called a simulation.
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Write a statement that correctly describes the relationship between these two sequences: 2, 4, 6, 8, 10 and 1, 2, 3, 4, 5. i really need help
Answers
The first series is an arithmetic sequence with a common difference 2, for the second series is an arithmetic sequence with a common difference 1.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
For the first sequence:
2, 4, 6, 8, 10
The above sequence represents the arithmetic sequence
The common difference = 4 -2 = 8 - 6 = 2
For the second series:
1, 2, 3, 4, 5
The above sequence represents the arithmetic sequence
The common difference = 2 -1 = 4 - 3 = 1
Thus, the first series is an arithmetic sequence with a common difference 2, for the second series is an arithmetic sequence with a common difference 1.
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Show that a/(b+1) - a/(b+1)^2 can be written as ab/(b+1)^2
Answers
Step-by-step explanation:
\( \dfrac{a}{b+1} - \dfrac{a}{(b+1)^2} = \)
\( = \dfrac{b + 1}{b + 1} \times \dfrac{a}{b+1} - \dfrac{a}{(b+1)^2} \)
\( = \dfrac{a(b + 1)}{(b+1)^2} - \dfrac{a}{(b+1)^2} \)
\( = \dfrac{ab + a}{(b+1)^2} - \dfrac{a}{(b+1)^2} \)
\( = \dfrac{ab + a - a}{(b+1)^2} \)
\( = \dfrac{ab}{(b+1)^2} \)
Answer:
Proof
Step-by-step explanation:
\( \frac{a}{(b + 1)} - \frac{a}{ {(b + 1)}^{2} } \)
Multiply the first fraction (the numerator and the denominator) by
\((b + 1) \\\)
In order to get common denominators for both fractions
\( \frac{a(b + 1)}{ {(b + 1)}^{2} } - \frac{a}{ {(b + 1)}^{2} } \)
Then expand the first fraction's numerator and subtract fractions to get your answer
\( \frac{ab + a}{ {(b + 1)}^{2} } - \frac{a}{ {(b + 1)}^{2} } = \frac{ab}{ {(b + 1)}^{2} } \)
6 tractors take 7 days to collect
the harvest.
How long would it take 9
tractors to do the same work?
Answers
Answer:
= 1.75
Step-by-step explanation:
7/6 divided by 6
= 7/36
7/36 = x/9
Cross multiply fractions:
36x = 63
Divide each side by 36:
x = 7/4 or 1.75
10 points please help i will report any links Factor the following polynomials. a6- 16
Answers
Answer:
The answer to your problem is -10
The equation of a plane passing through P(2,-3,-3) and is parallel to z= Zy is
Answers
The equation of a plane passing through P(2,-3,-3) and is parallel to z= Zy is z = -3.An equation of a plane is defined as the algebraic expression of a plane in terms of x, y, and z coordinates.
The general form of an equation of a plane is Ax + By + Cz = D.What is parallel to the plane?In mathematics, when two lines lie on the same plane or are in the same plane, they are known as parallel planes. As a result, in the equation of a plane, the plane equation z = k is parallel to the XY plane. Similarly, the plane equation y = k is parallel to the XZ plane, and the plane equation x = k is parallel to the YZ plane.What is z= Zy?The equation z = Zy is a plane parallel to the XY plane. The variable z is fixed at a certain value, and as a result, the plane extends indefinitely in both the X and Y directions.The given plane is parallel to z = Zy, therefore, the equation of a plane passing through P(2,-3,-3) and is parallel to z= Zy is z = -3.
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Rafi has $6,629 in an account that earns 10% interest compounded annually.
To the nearest cent, how much interest will he earn in 4 years?
Answers
The amount of interest would be $3076.51 in the account after 4 years.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
A = P(1+r/100)ⁿ
Where:
A = the future value of the investment or loan
P = the principal investment or loan amount
r = the interest rate (decimal)
n = the number of compound periods
Given that Rafi has $6,629 in an account that earns 10% interest compounded annually.
p = $6,629
r = 10%
t = 4 years
A = P(1+r/100)ⁿ
Substitute the values of p,r, and t in the formula,
A = 6,629 (1 + 10/100)⁴
A = 6,629 (1 + 0.10)⁴
A = 6,629 (1.1)⁴
A ≈ 9705.51
Now, C.I. = A - P
So C.I. = 9705.51 - 6,629 = $3076.51
Therefore, the amount of interest would be $3076.51 in the account after 4 years.
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14 POINTS AND BRAINLIEST EASY QUESTION LOOK AT IMAGES BELOW. THANKS!
Answers
Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ = 20 suggested in the article "Dynamic Ride Sharing: Theory and Practice"T). (Round your answer to three decimal places) (a) What is the probability that the number of drivers will be at most 19? (b) What is the probability that the number of drivers will exceed 29
Answers
a) The probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.
b) The probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.
(a) To find the probability that the number of drivers will be at most 19, we need to use the Poisson distribution formula:
P(X ≤ 19) = e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!) + ... + e^(-20) * (20^19/19!)
Using a calculator or statistical software, we get P(X ≤ 19) ≈ 0.088.
(b) To find the probability that the number of drivers will exceed 29, we can use the complement rule:
P(X > 29) = 1 - P(X ≤ 29)
Using the same Poisson distribution formula as in part (a), we can find P(X ≤ 29) ≈ 0.963. So,
P(X > 29) = 1 - 0.963 = 0.037 (rounded to three decimal places).
Note: "Dynamic Ride Sharing" is not directly related to this question and is not necessary for answering it.
Hi! I'd be happy to help you with your question.
(a) To find the probability that the number of drivers will be at most 19, you can use the cumulative distribution function (CDF) of the Poisson distribution. The parameter for this distribution is μ = 20. The formula for the Poisson CDF is:
P(X ≤ k) = Σ (e^(-μ) * (μ^x) / x!) for x = 0 to k
In this case, k = 19. Plugging in the values and calculating the sum, we get:
P(X ≤ 19) ≈ 0.411
Therefore, the probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.
(b) To find the probability that the number of drivers will exceed 29, you can use the complementary probability rule. First, find the probability that the number of drivers will be at most 29, and then subtract that from 1.
P(X > 29) = 1 - P(X ≤ 29)
Using the Poisson CDF formula with k = 29 and μ = 20:
P(X ≤ 29) ≈ 0.996
Now, subtract this value from 1:
P(X > 29) = 1 - 0.996 ≈ 0.004
Therefore, the probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.
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Write a multiplication equation and a division equation to represent each sentence or diagram.
A- There are 12 fourths in 3.
B- How many 2/3s are in 6?
Answers
Answer:
A) 3 = 12(1/4)
B) 6 = 2/3x
Step-by-step explanation:
A: 3 = 12(1/4)
3 = 12 fourths
B: 6 = 2/3x
x=9
Correct answer get brainliest and 5 star
Answers
Answer:
B
Step-by-step explanation:
(Slant height)^2= (Radius)^2+(Height)^2
(20)^2= (12)^2+(Height)^2
Height=16
Answer:
B. pls mark me at brainliest and like my answer.
Step-by-step explanation:
⩥ɓeŋʝ⩤
What do you call the point where a perpendicular bisector crosses another line?
Answers
Answer:
If AB crosses at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types. For obvious reasons, the point F is called the midpoint of the line PQ. See also Angle bisector.