Question

9. You are standing on a mountain that is 6842 feet high. You are looking down at your campsite, creating an angle of depression of 38°. If your eyes are 5.6 feet above the mountain how far is the base of the mountain from the campsite? (Round to the nearest hundredth)

Answer 1

Answer:

8,764.53 feet

Step-by-step explanation:

See the attached figure which represents the question.

Let the distance between campsite and the base of the mountain = d

The total height = 6842 + 5.6 = 6,847.6 feet.

As shown at the graph, the angle x and the depression angle are alternate angles, so they are congruent.

∴∠x = 38°

tan x = opposite/adjacent = (total height)/d = 6847.6/d

So, d = 6847.6/tan x

        = 6847.6/tan 38° = 8,764.53 feet (to the nearest hundredth)

so, the distance between campsite and the base of the mountain = 8,764.53 feet