Solving for Side Lengths of Right Triangles — Unit test Answers

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.

The hypotenuse of a 45°-45°-90° triangle measures in.

Triangle Q R S is shown. Angle Q R S is a right angle. Angle R S Q is 30 degrees and angle S Q R is 60 degrees. The length of R S is 5 StartRoot 3 EndRoot, the length of S Q is 10, and the length of R Q is 5.

The hypotenuse of a 45°-45°-90° triangle measures units.

Triangle R S T is shown. Angle T R S is a right angle. The length of R T is 5, the length of R S is 12, and the length of hypotenuse S T is 13.

Triangles A B C and X Y Z are shown. Angles A B C and X Y Z are right angles. Angles B A C and Y X Z are congruent. The length of A B is 5, the length of A C is 13, and the length of B C is 12.

The equation can be used to find the length of .

The law of cosines is used to find the value of m.

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.

Law of cosines: a2 = b2 + c2 – 2bccos(A)

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.

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.

The equation can be used to find the length of .

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x.