Question

A surveyor standing 100 meters from a bridge. She determines that the angle of the elevation to the top of the bridge is 35°. The surveyor's eye level is 1.45 meters above ground. What is the height of the bridge?

Answer 1

The height of the bridge is 71.47 m.

Explanation:

The angle of elevation `35^o` and the distance 100mcan be used to form a right triangle with the height of the bridge being the second leg.
We can us the trigonometric function tangent to solve for the sides of the triangle.

`tan 35^o = H/100`
`100tan35^o = H`
`100(0.7002) = H`
`70.02 = H`

Since the eye of the surveyor is 1.45m creating the horizontal distance, we must add the 1.45 m to the 70.02 m to determine the total height of the bridge.

`70.02 m + 1.45 m = 71.47 m`

The height of the bridge is 71.47 m.