trigonometry
posted by Winsel on .
From a mountain 1780 ft. high, the angle of depression of a point on the nearer shore of a river is 48deg40mins and of point directly across on the opposite side is 22deg20mins. What is the width of the river between the two points?

The height of the mountain is represented by the ver. side of a rt triangle. The line of sight of the 48
deg. angle represents the hypotenuse.
The hor. side is X.
A 2nd rt triangle
is formed by the line of sight of the
22 deg. angle, and its' ver. side is also the height of the mountain. the
hor. side = X + W where W is the width of the river.
Tan(48,40min) = 1780/X, X = 1565.6 Ft
Tan(22,20min) = 1780/(1565.6+W).
1565.6 + W = 1780/Tan(22,20min),
W = 2767.3 Ft. = Width of river. 
from the top of a mountain 532 m higher than a nearly river, the angle of depression of a point P on the closer bank of the river is 52.6o and the angle of depression of a point Q directly opposite. on P in the other side is 34.5o points P,Q and the foot of the mountain are on the same horizontal line. find the distance across the river from P to Q