Question

A boat heading out to sea starts out at Point A, at a horizontal distance of 804 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse beacon-light from that point to be 12^∘ . At some later time, the crew measures the angle of elevation from point B to be 2^∘ . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.

Answer 1

Answer: 672 feets

Step-by-step explanation:

Using the solution diagram attached, the vertical height, h of the lighthouse ;

Using trigonometry :

Tanθ = opposite / Adjacent

Tan 2 = h / 804

h = tan 2 * 804

h = 28.076 feets

Using h, we can obtain the distance CB :

Tan θ = opposite / Adjacent

Tan 2 = 28.076 / CB

CB = 28.076 / Tan 12°

CB = 132.08860 feets

Distance between A and B

804 - 132.08860

= 671.9 feets