Question

A boat is heading towards a lighthouse, where

Jeriel is watching from a vertical distance of 113
feet above the water. Jeriel measures an angle of
depression to the boat at point A to be 8°. At
some later time, Jeriel takes another
measurement and finds the angle of depression
to the boat (now at point B) to be 52°. Find the
distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.

Answer 1

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Answer 2

The distance from point A to point B, obtained using trigonometric ratios for tangent is about 715.7 feet

The steps used to find the distance can be presented as follows;

The height from which Jeriel measures the angle of depression to the boat is 113 feet

The angle of depression from the lighthouse to the boat at point A = 8°

Distance, d₁, of the boat at point A from the base of the lighthouse therefore can be found as follows;

tan(90 - 8) = d₁/113

d₁ = 113 × tan(90 - 8)

d₁ ≈ 804.0 ft

The angle of depression from the lighthouse to the boat at point B = 52°

Distance, d₂, of the boat at point B from the base of the lighthouse therefore can be found as follows;

tan(90 - 52) = d₂/113

d₂ = 113 × tan(38)

d₂ ≈ 88.3 ft

The distance from point A to point B is therefore;

Distance is; 804.0 - 88.3 = 715.7 feet