Question

A Scout on top of a 1500-ft. mountain spots a campsite.

if he measures the angle of depression at 33°, how far is the campsite from the foot of the mountain to the nearest foot?
please help
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Answer 1

Answer: The distance from the campsite to the foot of the mountain is 2310 ft (approx)

Step-by-step explanation: We have been given that the scout on the mountain top has spotted a campsite and he did so while looking down from a 33° angle of depression. If we label his position as point A, the foot of the mountain as point B and the campsite as point C, then it means the scout has formed an angle of 57° between point A and point B. Now we have a right angled triangle ABC with angle A measuring 57°

Using the trigonometrical ratio of tangent

Tan A = opposite/adjacent

Tan 57 = BC/1500

1.5399 = BC/1500

When you cross multiply both sides you have

1.5399 × 1500 = BC

2309.85 = BC

Approximated to the nearest foot,

BC = 2,310 ft