Question

A bridge is 70m long. From the ends of the bridge the angles of depression of a point on a river under the bridge are 41 degrees and 48 degrees. How high is the bridge above the river?

Answer 1

The point is obviously not under the MIDDLE of the bridge because the angles are not equal. I will assume however that it is directly under the bridge.

Let x be the distace by which the point is displaced from being below the middle of the bridge. Let h be the height of the bridge.

h/(35 + x) = sin 41

h/(35 - x) = sin 48

(35-x)/(35+x) = sin 41/sin48 = 0.88281
35 - x = 30.899 + .88281x

Solve for x and then solve for h.

Answer 2

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