How Do You Calculate the Height of a Building Using Trigonometry?

[illmatic899]

A surveyor stands on flat ground at an unknown distance from a tall building. She measures the angle from the horizonal ground to the top of the building; this angle is pi/3. next she paces 40ft further away from the building. the angle from the ground to the top of the building is now measured to be pi/4.
a)how tall is the building
b) If the surveyor moves 20 feet further from the building what will the angle from the horizontal to the building's roof be.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Let the height of the building, in feet, be h, the initial distance from the building be x. Then you have $tan(\pi/3)= \sqrt{3}= x/h$. 40 ft further away, the building is still h feet high and the distance from the building is now x+ 40 feet. Now you have $tan(\pi/4)= 1= (x+40)/h$. You now have two equations to solve for x and h.

For (b), let $\theta$. You have already solved for x so you know the distance from the building is x+ 40+ 20. And, of course, you have solved for h. Now, $tan(\theta)= (x+ 60)/h$. Solve that equation for $\theta$.