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?

Answer 1

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.

Answer 2

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