Q10. To the nearest tenth, what is the length of Side a in the triangle below?

Background

Topic: Right Triangle Trigonometry

This question tests your ability to use trigonometric ratios (sine, cosine, tangent) to find the length of a side in a right triangle when given an angle and another side.

Key Terms and Formulas

• Opposite side: The side across from the given angle (here, side a is opposite the 33° angle).

• Adjacent side: The side next to the given angle (here, 45.2 in is adjacent to the 33° angle).

• Tangent function:

Step-by-Step Guidance

1. Identify the given values: The angle and the adjacent side in.

2. Recognize that you are looking for the length of the side opposite the angle (side ).

3. Set up the tangent ratio for the given angle:

4. Rearrange the equation to solve for :

Try solving on your own before revealing the answer!