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

Triangle A B C is shown. The length of A B is 12, the length of B C is 24, and the length of C A is 12 StartRoot 3 EndRoot

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.

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.

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.Law of sines:

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

Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch.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.

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand.Law of cosines:

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?

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.

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.

Heron’s formula: Area =

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 equation can be used to find the length of .

The equation can be used to find the length of .

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

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.

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