Q19. Use the following to solve the right triangle. Give angles in degrees and minutes. Round side lengths to two decimal places.

Background

Topic: Right Triangle Trigonometry

This question tests your ability to use trigonometric relationships and the Pythagorean theorem to solve for unknown sides and angles in a right triangle, given one angle and one side.

Key Terms and Formulas:

• Right triangle: A triangle with one angle equal to 90°.

• Pythagorean Theorem:

• Trigonometric ratios:

• Sum of angles in a triangle:

Step-by-Step Guidance

1. Identify the given values: angle and side ft.

2. Recall that angle is since the triangle is a right triangle.

3. Calculate angle using the triangle angle sum: .

4. Use the sine and cosine ratios to set up equations for sides and :

5. Convert angle to decimal degrees if needed for calculation.

Try solving on your own before revealing the answer!