Question

Tristin is attempting to dive from an 8 foot diving board into a tube that is located 12 feet from the base of the diving board. What should be his angle of depression to ensure he hits the tube

Answer 1

Answer:

The angle of depression is 33.7°.

Step-by-step explanation:

To find the angle of depression, you need to form a triangle based on the given measurements and use trigonometric functions to solve for the angle.  In this case, the triangle is formed from a base of 12 feet (the horiontal distance from the tube to the base of the diving board) and a height of 8 feet (the height of the diving board).  The angle of depression is formed from the angle made from the tube in the water to the top of the diving board.  To find the measure of the angle, we get:

tan y = $\frac{opposite}{adjacent}$ or tan y = $\frac{8}{12}$

In order to find 'y', or the angle of depression, we need to take the inverse tangent of the fraction:

y = $tan^{-1}\frac{8}{12}$ or y = 33.7°.