Posted by **Winsel** on Tuesday, August 10, 2010 at 10:25am.

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?

- trigonometry -
**Henry**, Tuesday, August 10, 2010 at 11:49am
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.

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