A lighthouse keeper 100 feet above the water sees a boat sailing in a straight line directly toward her. As watches, the angle of depression to the boat changes from 25 degrees to 40. How far has the boat traveled during this time?

Answer 1

First, we draw a rectangle and label
the ver. sides 100ft and hor.(longer)
sides X ft. Then we draw a diag. from
upper left to lower rt. side forming a rt triangle. The angle of elevation = the angle of depression = 25deg.
Draw a 2nd line from upper left corner
to some point(near the center) on the
bottom hor. line forming an angle of
40deg with the hor. Label the 2 sections on the bottom line X1 and X2
(rt to lt).

tan25 = Y/X = 100/X,
X = 100 / tan25 = 214.45 ft.

tan40 = Y/X2 = 100/X2,
X2 = 100 / tan40 = 119.2ft.

X1 + X2 = X,
X1 + 119.2 = 214.5,
X1 = 214.5 - 119.2 = 95.3ft. = distance traveled.