SOLUTION: A 60-footpiece of wire is strung between the top of a tower and the ground, making a 30-60-90 triangle. How far from the center of the base of the tower is the wire attached to the

Algebra ->  Triangles -> SOLUTION: A 60-footpiece of wire is strung between the top of a tower and the ground, making a 30-60-90 triangle. How far from the center of the base of the tower is the wire attached to the      Log On


   

Question 373442: A 60-footpiece of wire is strung between the top of a tower and the ground, making a 30-60-90 triangle. How far from the center of the base of the tower is the wire attached to the ground?How high is the tower?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A 60-footpiece of wire is strung between the top of a tower and the ground, making a 30-60-90 triangle.
How far from the center of the base of the tower is the wire attached to the ground?How high is the tower?
:
Assume the 30 degree angle is wire angle to the ground
The guy wire is the hypotenuse (60 ft)
the side adjacent is the distance (d) from the tower to the tie point on the ground
the opposite side the height (h) of the tower
:
Use the sine of the angle to find the height of the tower; sin(a) = %28side+opposite%29%2F%28hypotenuse%29
sin(30) = h%2F60
60*.5 = h
h = 30 ft is the height of the tower
:
Use the cosine to find d; cos(a) - %28side+adjacent%29%2F%28hypotenuse%29
cos(30) = d%2F60
60 * .866 = d
d = 52 ft distance from tower to tie point