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# Right Triangle Trigonometry Exercise 2

## Reference Triangle

## Instructions for Exercise 2

Here is the second of three examples. Use the triangle to the right for reference. The solution is at the bottom of the post. A trig table and the trig wheels are also included.

The length of side A is 100, and the length of side C is 42. Find the length of the hypotenuse and angles 1 and 2.

## Solution for Exercise 2

This solution demonstrates one of a number of possible ways to come to the values in **bold**; the important thing is to arrive at the same values shown for each unknown.

The length of side A is 100, and the length of side C is 42. Find the length of the hypotenuse and angles 1 and 2.

Angle 1 can be found by dividing opposite side 42 by adjacent side 100. The tangent of **angle 1** is 0.42. The table shows that the angle associated with a tangent of .42 **is (approx.) 23°**.

Angle 2 is found by subtracting 23° from 90°. **Angle 2 is 67°**.

The hypotenuse (side B) is found by taking the side adjacent to angle 1 (side A), 100, and dividing it by the cosine of angle 1 (angle 1 is 23°, therefore the cosine is 0.9205). **Side B is equal to 100/.9205 or 108.64**.