An observer at the top of a 462-ft cliff measures the angle of depression from the top of the cliff to a point on the ground to be 5°. What is the distance from the base of the cliff to the point on the ground?

The distance from the base of the cliff to the point on the ground is 5,280.7 ft.

The given parameters;

The distance from the base of the cliff to the point on the ground is calculated as follows;

Thus, the distance from the base of the cliff to the point on the ground is 5,280.7 ft.

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complete question:

An observer at the top of a 462-ft cliff measures the angle of depression from the top of the cliff to a point on the ground to be 5°. What is the distance from the base of the cliff to the point on the ground? Round to the nearest foot

a ≈  5281 ft

Explanation:

The observer at the top of a 462 ft cliff  measures the angle of depression from the top of the cliff to a point on the ground to be 5°.

The angle of depression form the top of the cliff = 5°

The 5° is outside the triangle formed . To find the angle in the triangle we have to subtract 5° from 90°.  90° - 5° = 85° Note sum of an angle on a right angle is 90°.  

using SOHCAHTOA  principle we can solve for the distance from the base of the cliff to the point on the ground(a)

tan  85° = opposite / adjacent

tan 85°  = a / 462

cross multiply

462 × tan 85° = a

a = 11.4300523 × 462

a =  5280.66  ft

a ≈  5281 ft