Question

A boat heading out to sea starts out at Point A, at a horizontal distance of 1315 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 12°. At some later
time, the crew measures the angle of elevation from point B to be 8°. Find the
distance from point A to point B. Round your answer to the nearest foot if
necessary.

Answer 1

Answer: 674 ft

Explanation:

`\tan 12^(\circ)=(y)/(1315) \\ \\ 1315\tan 12^(\circ)=y`

`\tan 8^(\circ)=(y)/(x+1315) \\ \\ (x+1315)\tan 8^(\circ)=y \\ \\ (x+1315)\tan 8^(\circ)=1315 \tan12^(\circ) \\ \\ x \tan 8^(\circ)+1315 \tan 8^(\circ)=1315 \tan 12^(\circ) \\ \\ x \tan 8^(\circ)=1315 \tan 12^(\circ)-1315 \tan 8^(\circ) \\ \\ x=(1315 \tan 12^(\circ)-1315 \tan 8^(\circ))/(\tan 8^(\circ)) \approx \boxed{674 \text{ ft}}`