# 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.

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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**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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