what is the height of the building?

Question

A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 28 degrees. He then moves back 54.4 feet and determines that the angle of elevation is 21.3 degrees. What is the height of the building?Round your answer to four decimal places.

Answer 1

The isocolies triangle comes first.

α=6.7°

β=21.3°

γ=152°

a=54.4'

You want sides b and c.

a/sinα=b/sinβ=c/sinγ

54.4/.1166=4663=169.37/.3633=b

?/.4695=4663=218.9=c

Right triangle:

a/sinα=b/sinβ=c/sinγ

b from above is now c for the rt tri.=169.37

Looking for side a.

?/.4695=169.37 a=79.5'

Note:180-6.7-21.3=152

90sin=1.

Answer 2

Draw and label a diagram

h is the height of the building

x is the distance from the building to first measurement

tan 28° = h / x

x tan 28° = h

tan 21.3º = h / (x + 54.4)

(x + 54.4) tan 21.3º = h

x tan 28º = (x + 54.4) tan 21.3°

Solve for x. Use that value to solve for h