Question

A boat heading out to sea starts out at Point A, at a horizontal distance of 1246 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 14°. At some later
time, the crew measures the angle of elevation from point B to be 5°. Find the
distance from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.

Answer 1

Answer:2304.9

Explanation:

Answer 2

2304.9 ft

Explanation:

You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.

Tangent

The tangent relation for sides in a right triangle is ...

Tan = Opposite/Adjacent

In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:

tan(14°) = h/1246

tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B

Solution

Solving these equations for d, we have ...

h = 1246·tan(14°) = (1246+d)·tan(5°)

d·tan(5°) = 1246·(tan(14°) -tan(5°))

d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet

The distance from point A to point B is about 2304.9 feet.

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