SOLUTION: A hawk is perched atop a 90 foot lamppost. A squirrel on the ground 60 feet from the base of the lamppost. Determine the angle of depression to the squirrel as observed by the haw

Question 1102454: A hawk is perched atop a 90 foot lamppost. A squirrel on the ground 60 feet from the base of the lamppost. Determine the angle of depression to the squirrel as observed by the hawk. How far is the squirrel from the hawk? If the hawk can fly 4 feet every second, how many seconds will the hawk take to swoop down to the squirrel?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's my diagram.
look below the diagram for further comments.

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what you see is rectangle ABCD.

the hawk is at A.
the bottom of the lamppost is at D.
the squirrel is at C.
AD is parallel and congruent to BC.
AB is parallel and congruent to DC.

angle 1 and angle 2 are congruent because they are alternate interior angles to parallel lines AB and DC.

angle 3 and angle 4 are congruent because they are alternate interior angles to parallel lines AD and BD.

the angle of depression from A to C is equal to angle 1.

since angle 2 is equal to angle 1, you can find the measure of angle 1 by finding the measure of angle 2.

the tangent of angle 2 is opposite / adjacent = 90 / 60.

the measure of angle 2 is the arc tangent of (90 / 60).

the measure of angle 2 is therefore equal to 56.30993245.

since this is the same as the measure of angle 1, then your angle of depression is equal to 56.30993245 degrees.

since angle ADC forms a right triangle, then you can find the length of AC by using the pythagorus formula.

AC is therefore equal to square root of (90^2 + 60^2) which makes AC equal to 108.1665383 feet.

AC is the distance from A to C which is the distance from the hawk to the squirrel since the hawk is at A and the squirrel is at C.

if a hawk can fly at a speed of 4 feet per second, then it would take the hawk 108.1665383 / 4 = 27.04163457 seconds to reach the squirrel.

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