Posted by **Chloe Mack** on Sunday, January 30, 2011 at 7:44pm.

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?

- Pre-Calculus-Trig -
**Henry**, Monday, January 31, 2011 at 8:44pm
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.

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