PreCalculusTrig
posted by Chloe Mack on .
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?

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.