Question

A boat heading out to sea starts out at Point AA, at a horizontal distance of 1347 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 9^{\circ}
∘
. At some later time, the crew measures the angle of elevation from point BB to be 3^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer 1

The distance from point A to B is 2723.8 feet.

Trigonometric ratio

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the height of the light house, hence:

tan(9) = h/1347

h = 213.3 feet

Let d represent the distance from point B to the lighthouse base, hence:

tan(3) = 213.3/d

d = 4070.8 feet

Distance from point A to B = 4070.8 feet - 1347= 2723.8 feet.

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