right triangle relationships unit test review

Given △ABC ~ △XYZ, what is the value of cos(Z)?

12/13

The equation cos(35o) = can be used to find the length of . What is the length of ? Round to the nearest tenth.

20.5 in.

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image. What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7

Given right triangle QRS, what is the value of sin(30°)?

1/2

The equation tan(55o)=can be used to find the length of . What is the length of ? Round to the nearest tenth.

10.5 cm.

The hypotenuse of a 45°-45°-90° triangle measures in. What is the length of one leg of the triangle?

5 ^/10

Given right triangle RST, what is the value of sin(S)?

5/13

Which is the best approximation for the measure of angle ABC?

58.3 degrees

Which is the best approximation for the measure of angle ABC?

58.3°

The hypotenuse of a 45°-45°-90° triangle measures units. What is the length of one leg of the triangle?

7 units

What are the angle measures of triangle ABC?

m∠A = 90°, m∠B = 60°, m∠C = 30°

Which equation can be used to find the measure of angle LKJ?

sin-1(8.9/10.9)=x

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet. What is the distance around the perimeter of the garden?

120ft.

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.

14.2 feet

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number.

183 meters