Question

A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 10^{\circ} ∘ , before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 21^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer 1

The distance between points A and B and the boat is an illustration of elevation and distance

The distance from point A to point B is 346 feet

How to calculate the distance AB

The height of the lighthouse is given as:

h = 113

The distance between point A and the base of the lighthouse is calculated using the following tangent ratio

$\tan(10) = \frac{113}{A}$

Make A, the subject

$A = \frac{113}{\tan(10)}$

$A = 640.85$

The distance between point B and the base of the lighthouse is calculated using the following tangent ratio

$\tan(21) = \frac{113}{B}$

Make B, the subject

$B= \frac{113}{\tan(21)}$

$B= 294.38$

The distance AB, is then calculated as:

$AB = A - B$

$AB = 640.85 - 294.38$

$AB = 346.47$

Approximate

$AB = 346$

Hence, the distance from point A to point B is 346 feet

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