Question

While surveying Overlook Cave, Mike measures the angle of elevation from his line of sight to the top of a rock formation as 22°. The rock formation is 10 feet away and he is measuring from a point 3 feet above the floor of the cave. To the nearest tenth of a foot, how high is the rock formation?

Answer 1

The rock formation is approximately 7 feet tall.

Explanation:

We can visualize this situation as a triangle and know that the bottom side is 10 and the angle of elevation (the angle created by Mike and the ground, looking to the top of a rock). With this information, we can use tangent to solve.

x = the height of the rock formation

tan(22°) = x/10

10 tan(22°) = x

x = ~4.04 feet

We also have to add the 3 feet to it because it is being measured 3 feet above the floor.

x + 3 = 7.04 feet