Angle of Depression Problems

Introduction to Angle Of Depression problems:

The word “depression” means “fall” or “drop”.

Angle of depression problem is the angle which is between the horizontal and the line of sight to an object beneath the horizontal. The angle of Depression is similar to angle of elevation.

The angle of depression problem is below the horizontal that an observer must look to see an object that is lower than the observer.The angle of depression is similar to the angle of elevation (this assumes the object is close to the observer so that the horizontals for the observer and the object are parallel; this would not be the case for an astronaut in orbit around the earth observing an object on the ground).

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Angle of depression problem:1

A man who is 2 meter tall stands on horizontal ground 30 meter from a tree. The angle of elevation from the top of the tree from his eyes is 28˚. Find the height of the tree.

Angle of depression problem solution:

Let the height of the tree be h.
Tan 28o=(h-2)/30
h – 2 = 30 tan 28˚
h = (30 ´ 0.5317) + 2 ← tan 28˚ = 0.5317
= 17.951
The height of the tree is approximately 17.95 meter.

Angle of depression problem:2

An Bird is flying at an altitude of 1000 m. The angle of depression from the bird of a tree on the ground is measured as 15°. What is the distance from the bird to the tree?
Choices:
A. 3,864 m
B. 3,732 m
C. 1,035 m
D. 1,000 m
Angle of depression problem solution:
Step 1: Let x be the distance from the bird  to the tree.
Step 2: Here the horizontal lines are parallel; the angles of elevation is equal to angle of depression Step 3: sin 150=1000/x
Step 4: x=1000/sin 150
Step 5: x = 3,864 m
Step 6: the distance from the bird to the tree is 3,864 m.