# Math

In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If the sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?

1. 👍
2. 👎
3. 👁
1. sin A = 1/2
A = 30 degrees

sin is opposite over hypotenuse thus, BC/AC
BC = 8 (given)

thus 1/2 = 8/AC
AC = 16

cos A is cos 30degrees so cos A = (sqrt(3)) / 2

cos is always adjacent over hypotenuse thus, AB/AC
because AC = 16

sqrt3 /2 = AB/16

AB = 8 sqrt3

1. 👍
2. 👎

## Similar Questions

1. ### math

1. What is the correct classification for the triangle shown below? A triangle has two angles measuring 68 degrees and 22 degrees. (1 point) acute, scalene acute, isosceles --- right, scalene obtuse, scalene 2. What is the value

2. ### Geometry

In the triangle, angles ABC and ADE are right angles. If AC = 35, AE = 11, and BE = 10, then what is AD?

3. ### math

Triangle ABC undergoes a series of transformations to result in triangle DEF. Is triangle DEF congruent to triangle ABC ? Is it Congruent or Not congruent? 1.)) Triangle ABC is translated 3 units up and 5 units right, and then

4. ### geometry

triangle abc is similar to def, the lengths of the sides of triangle abc is 5,8,11. what is the length of the shortest side of triangle def if its perimeter is 60?

In triangle ABC, D bisects side BC, G bisects side AB, and the points E and F trisect side AC. What is the area of the shaded polygon, if the area of ABC is 108? I tryed to find the area of triangles on the side and I figured that

2. ### Algebra

Question 1 A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of

Which of the statements about the picture below is true? Choose 3. postimg(.)org/image/qb71bjkjh/f11870c4/ A. F is the circumcenter of the triangle

4. ### HELP!!!!RIGHT NOW!!!!

Which set of side lengths shows similar triangles? (1 points) A) Triangle ABC : 40, 20, 50; Triangle XYZ: 10, 4, 8 B) Triangle ABC : 30, 20, 60; Triangle XYZ: 40, 60, 90 C) Triangle ABC : 110, 80, 60; Triangle XYZ: 6, 8, 5.5 D)

1. ### Math

Triangle ABC has angles measuring 137°, 15°, and 28°. Classify the triangle by its angle measures. right triangle acute triangle obtuse triangle multiangular triangle I thinks it's c

2. ### Geometry

1. Given: R and T are right angles and SV bisects RST Prove: RSV = TSV R and T are right angles / given R = T/ All right angles are congruent SV bisects RST/ given 1 = 2 / definition of angle bisector SV = SV / reflexive property

3. ### geometry

find the value of x in each triangle: triangle x has 1 angle at 53 degree for value x i got: 63.5 degree is that correct? Classify each triangle. 7. The measures of 2 angles are : 45 degree and 45 degree i got: acute 8. the

4. ### Math

Classify the triangle by its angles and its sides. Explain how you knew which classifications to use. Cant add images but the angles are 70, 65 and 45. It's an acute triangle? I'm not sure what the question is asking but if my