Unit 6 Test for Chapter 9

Given side lengths of 6, 8, and 12 classify the triangle.

Note: a² + b² = c²

Find the exact length of side BC.

Note: a² + b² = c²

Find the measure of angle A. Round to the nearest tenth.

Note: Use your calculator for sin^-1, cos^-1, or tan^-1 .

Which trigonometric ratio would be used to solve for the value of side q?

Note: SOH-CAH-TOA

Find the measure of the unknown angle.

Note: The sum of the angles inside the triangle.

What is the trigonometric ratio for sin D?

Note: SOH-CAH-TOA

Find the exact value of segment IR.

Note: Label the S, L, and H sides before you choose the formula.

1. Find the exact value of segment TI.

Note: Label the S, L, and H sides before you choose the formula.

A right triangle has a base of 12 m and a height of 5m, find the length of the hypotenuse.

Note: a² + b² = c²

In the diagram, △ABC is similar to △DEF. The area of △ABC is 36 cm², find the area of △DEF.

Note: Similar triangles have a scale factor. Their perimeters are proportional to the scale factor. Their areas are proportional to the square of the scale factor.

A sonar operator on a ship detects a submarine at a distance of 500 meters and an angle of depression of 40˚. How deep is the submarine to the nearest meter?

Hint: SOH-CAH-TOA

The sun casts a shadow of a man on the ground that is 5.45 feet long. The angle of elevation is 50˚.

What is the height of the man? Round your answers to the nearest hundredth.

Hint: SOH-CAH-TOA

You lean a 20 foot ladder against a wall. The base of the ladder is 4 feet from the wall. Safety

guidelines require the angle of elevation of the ladder from the ground to be between 70⁰ and 75⁰.

Does the angle 𝜃 meet the safety guideline? Explain your answer.

Hint: SOH-CAH-TOA

Given the diagonal of the square is 10 cm. What is the exact length of each side a?

Note: Label your the sides with L and H before choosing a formula.

What is the perimeter of the square to the nearest cm?

Note: Use your answer from problem 14 to help you.

What is the area of the square to the nearest square inch?

Note: Use your answer from problem 14 to help you.