Question

Suppose a person is standing on the top of a building and that she has an instrument that allows her tomeasure angles of depression. There are two points that are 100 feet apart and lie on a straight line that isperpendicular to the base of the building. Now suppose that she measures the angle of depression from thetop of the building to the closest point to be 34.5 and the angle of depression from the top of thebuilding to the furthest point to be 27.8°. Determine the height of the building. (Round your answer to thenearest tenth of a foot.)

Answer 1

see the figure below to better understand the problem

In the right triangle ABC

tan(34.5)=h/x -----> by TOA

h=x*tan(34.5) -----> equation 1

In the right triangle ABD

tan(27.8)=h/(100+x) -----> by TOA

h=(100+x)*tan(27.8) -----> equation 2

Equate equation 1 and equation 2

x*tan(34.5)=(100+x)*tan(27.8)

solve for x

x*tan(34.5)=100*tan(27.8)+x*tan(27.8)

x*[tan(34.5)-tan(27.8)]=100*tan(27.8)

x=329.4 ft

Find out the value of h

h=x*tan(34.5)

h=329.4*tan(34.5)

h=226.4 ft

therefore

the answer is

the height of the building is 226.4 ft