Calculating Building Height Using Trigonometry | Surveyor's Method

[anthonym44]

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.

The Attempt at a Solution

i think i got this one right, but I am new to the site so i thought i would just check myself with this problem. i got equation 40 + x = y beause the horizontal axis must equal the vertical when the angle is 45 degrees (pi/4). Then i used tan(60) = y/x to solve for x and then i subsituted eventually solving for y. my final answer is 94.8ft. part B asks for the angle if the person moves further back 20 ft. i just added that length to 94.8 and used tan to solve eventually getting the angle to be 39.5 degrees. If anyone has the time can they check the work to make sure i did it correctly? Thanks.

 

[Dick]

Yup, that's right. I get something closer to 94.6 ft for the height though.

 

[anthonym44]

thanks for your help Dick.