Law of Sines (Sec 8-3) — Unit test Answers

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.

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.

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.

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.

Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.Heron’s formula: Area

Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles.Triangle 1: 3 in., 6 in., 7 in.Triangle 2: 3 in., 6 in., 8 in.Triangle 3: 3 in., 7 in., 8 in.Triangle 4: 6 in., 7 in., 8 in.

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.

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.

Triangle A B C is shown. Angle A B C is a right angle. Angle B C A is 22 degrees and angle C A B is 68 degrees.

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

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.

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.

The equation can be used to find the length of .

Use the law of sines to find the value of a.Law of sines: