Question

An engineer stands 50 feet away from a building with a surveying device mounted on a tripod. if

the surveying device is 5 feet above the ground and the angle of elevation is 50°, find how tall is
the building.​

Answer 1

The building is 64.6 feet tall.

Explanation:

To determine the height of the building, let the height from the top of the building to the top of the tripod be represented by x. So that;

Height of the building = x + 5

But,

Tan θ =
`(opposite)/(adjacent)`

Tan
`50^(o)` =
`(x)/(50)`

x = 50 x Tan
`50^(o)`

= 50 x 1.1918

= 59.59

x = 59.59

Height of the building = x + 5

= 59.59 + 5

= 64.6 ft

The height of the building is 64.6 feet.