Math  trigonometry
posted by anonymous on .
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?

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
(35x)/(35+x) = sin 41/sin48 = 0.88281
35  x = 30.899 + .88281x
Solve for x and then solve for h. 
hlkh