SOLUTION: I am in desperate need of assistance with an application problem. Any help would be appreciated. The problem: A man at ground level measures the angle of elevation to the top of

Algebra ->  Trigonometry-basics -> SOLUTION: I am in desperate need of assistance with an application problem. Any help would be appreciated. The problem: A man at ground level measures the angle of elevation to the top of      Log On


   

Question 143742: I am in desperate need of assistance with an application problem. Any help would be appreciated.
The problem:
A man at ground level measures the angle of elevation to the top of a building to be 53 degrees . If, at this point, he is 12 feet from the building, what is the height of the building? I need find the solution to the nearest hundredths and draw the picture. The same man now stands atop a building. He measures the angle of elevation to the building across the street to be 20 degrees and the angle of depression (to the base of the building) to be 35 degrees. If the two buildings are 50 feet apart, how tall is the taller building? Round to the nearest hundredths.


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A man at ground level measures the angle of elevation to the top of a building to be 53 degrees . If, at this point, he is 12 feet from the building, what is the height of the building? I need find the solution to the nearest hundredths and draw the picture.
:
Draw a right triangle, Let x = the height of the building, then 12 ft from the base of the building to where the man stands and the hypotenuse is from that
point to the top of the building.
:
We can find the height of the building by using the tangent of 53 degrees
Tan = side+opposite%2Fside+adjacent
Tan(53) = x%2F12
1.327045 = x%2F12
x = 12 * 1.327045
:
x = 15.9245 ~ 15.92 ft
:
:
The same man now stands atop a building. He measures the angle of elevation to the building across the street to be 20 degrees and the angle of depression (to the base of the building) to be 35 degrees. If the two buildings are 50 feet apart, how tall is the taller building? Round to the nearest hundredths.
:
Draw this out and see that you have two right triangles with a common side of 50'
Find the
tan(20) = x1%2F50
.36397 = x1%2F50
x1 = .36397 * 50
x1 = 18.20 ft
and
tan(35) = x2%2F50
.7002 = x2%2F50
x2 = .7002 * 50
x2 = 35.01 ft
:
Add these two values:
18.20 + 35.01 = 53.21 ft is the height of the building