A boat heading out to sea starts out at Point A, at a horizontal distance of 1462 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 7º. At some later time,
the crew measures the angle of elevation from point B to be 3º. Find the distance
from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
see the picture below to better understand the problem
we have that
tan(3)=h/(1462+x) -----> h=(1462+x)*tan(3)
tan(7)=h/1462 -----> h=1462*tan(7) -----> h=179.5 ft
Find the value of x
h=(1462+x)*tan(3) -----> 179.5/tan(3)=1462+x ----> x=1,963.1 ft
therefore
the distance AB is 1,963.1 ft