Right Triangle Review

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

• $\cos^{-1}\left(\frac{8.9}{10.9}\right)=x$

• $\cos^{-1}\left(\frac{10.9}{8.9}\right)=x$

• $\sin^{-1}\left(\frac{8.9}{10.9}\right)=x$

• $\sin^{-1}\left(\frac{10.9}{8.9}\right)=x$

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

• $27.7\degree$

• $31.7\degree$

• $58.3\degree$

• $62.3\degree$

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

At approximately what angle does the wire meet the ground?

• 33.6°

• 39.8°

• 50.2°

• 56.4°

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°

• 17.5°

• 72.5°

• 73.3°

The equation $\cos\left(35\degree\right)=\frac{a}{25}$ can be used to find the length of  $\overline{BC}$ .

What is the length of segment BC? Round to the nearest tenth. 

• 14.3 in.

• 20.5 in.

• 21.3 in.

• 22.6 in.

The equation $\tan\left(55\degree\right)=\frac{15}{b}$ can be used to find the length of  $\overline{AC}$ .

What is the length of   $\overline{AC}$ ? Round to the nearest tenth. 

• 3.0 in.

• 9.8 in.

• 10.5 in.

• 12.8 in.

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

• 250 meters

• 366 meters

• 683 meters

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 25 degree angle with the ground and when the string makes a 45 degree angle with the ground? Round to the nearest tenth.

• 14.2 feet

• 17.1 feet

• 47.6 feet

• 55.2 feet

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

• 5/13

• 5/12

• 12/13

• 13/12

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

• $\frac{\sqrt{3}}{3}$

• $\frac{1}{2}$

• $\frac{\sqrt{3}}{2}$

• $\frac{2}{1}$