From the bottom of a canyon Rita stands 47m directly below an overhead bridge. She estimates that the angle of elevation of the bridge is about 35 degrees at the north end and about 40 degrees at the south end. If the bridge were level how long would it be?
Rita stands directly below the overhead bridge that is at a height of 47 m. The angle of elevation of the North and South ends of the bridge is 35 degrees and 40 degrees respectively.
The problem involves two triangles. One is formed by the vertical line from Rita to the bridge above here, the line joining the point vertically above Rita to the North end and the line joining Rita to the North end. As the angle of elevation of the North end is 35 degrees, the angle between the hypotenuse of the triangle and the vertical line is 90 - 35 = 55 degrees. The length of this segment of the bridge is 47*tan 55 = 67.12 m. Similarly the length of the other segment is 47*tan(90 - 40) = 47*tan 50 = 56.01 m. Adding the two gives the length of the bridge as 123.13 m
The length of the bridge is 123.13 m