# A wire is stretched from ground to the top of an antenna tower?

A wire is stretched from ground to the top of an antenna tower. The wire is 20ft long. The height of the tower is 4 ft greater than the distance d from the towers base to the bottom of the wire. Find the distance d and the height of the tower.

Answer:
this forms a right triangle with hypothenus 20, height d+4, and base d.
Using the pythagorean theorem we get:
(d+4)² + d² = 20²
d² + 8d + 16 + d² = 400
2d² + 8d + 16 = 400
2d² + 8d - 384 = 0
Use the quadratic equation to solve for d
d = [-8±√(8²-4∙2∙(-384) )] / 2∙2
for which we get d = -16 (reject because negative) and
d = 12
height = d + 4 = 16
note that 12²+16² = 20²
distance d? haha sounds like you need to copy the picture off your homework :-)
im agreed with ignormaus. D is 12ft and height is 16ft. absolutely correct collection. d is the dist. d+ 4 is height. so the eq is now for right angle triangle is
d^2 + (d+4)^2 = 20^2.
d^2 + d^2 + 8d + 16 = 400
2d^2 + 8d - 384 = 0
d^2 +4d - 192 = 0
d^2 + 16d - 12d - 192 = 0
d(d+16) - 12(d+16) = 0
(d+16)(d-12) = 0
d= - 16, d = 12
hence d = -16 is not possible length belong to N set. so d=12 ft is solution. and total height is 16ft.

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