Question
A wire is stretched from the ground to the top of an antenna tower. The wire is 20 feet long. The height of the tower is 4 feet greater than the distance from the tower's base to the end of the wire. Find the height of the tower.
20 ft.= w
x.4 = height of tower
something like this?
20 ft.= w
x.4 = height of tower
something like this?
Answers
I must assume that the wire's base is attached at some distance from the bottom of the tower, like a "guy-wire".
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Let the tower's height be H and the length of the wire be L = 20.
Use the Pythagorean theorem:
20^2 = H^2 + (H-4)^2
and solve for H.
400 = 2 H^2 -8H + 16
H^2 -4H -192
(H-16)(H+12) = 0
Take the positive root, H = 16 feet.
The tower's base is sqrt (20^2 - 16^2) = 12 feet from where the cable touches the ground.
(Broken Link Removed)
Let the tower's height be H and the length of the wire be L = 20.
Use the Pythagorean theorem:
20^2 = H^2 + (H-4)^2
and solve for H.
400 = 2 H^2 -8H + 16
H^2 -4H -192
(H-16)(H+12) = 0
Take the positive root, H = 16 feet.
The tower's base is sqrt (20^2 - 16^2) = 12 feet from where the cable touches the ground.