Question

A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 34.8∘. He then moves back 57.3 feet and determines that the angle of elevation is 26.7∘
26.7. What is the height of the building?
Round your answer to four decimal places.
Height of building =

Answer 1

Answer:

we have two rectangle triangles formed; one has one leg equal to H and the other leg is x the elevation angle of the line from the ground to the top is 26.2 degrees. The other triangle has one leg equal to H and the other leg equal to (X+53.9). We have a common side which is H. So if we make the two H equal we will solve for x

as follows:

Tan 26.2 = (H/x) ; tan 18.9 = (H/(x+53.9), then x *tan 26.2=(x+53.9)*tan 18.9

We have the following equation:

0.4921x = 0.3424x + 18.45

0.1497 x = 18.45 => x= 123.25 feet

The height will be

Tan 26.2=H/123.25 from where H= 60.64feet

Check is:

Tan -1( 60.64)/(123.25+53.9) Then angle is 18.9 degrees