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A flagpole is secured on opposite sides by two guy wires, each of which is 5 ft longer than the pole. the distance between the points where the wires are fixed to the ground is equal to the length of one guy wire. how tall is the flagpole (to the nearest inch)?

User Johncosta
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1 Answer

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The height of the flagpole to the nearest inch is 388 inches.

Step-by-step explanation

According to the below diagram, AB is the flagpole which is secured on opposite sides by two guy wires, AB and AC.

Suppose, the length of the flagpole(AB) is
x ft.

As each of the guy wires is 5 ft longer than the pole, that means
AC= AD= (x+5)ft

Also given that, the distance between the points where the wires are fixed to the ground is equal to the length of one guy wire. That means,
CD= (x+5)ft

As
\triangle ABC and
\triangle ABD are congruent to each other, so
BC=BD= (1)/(2)CD= (1)/(2)(x+5) ft

Now in right triangle
ABD, using Pythagorean theorem......


AB^2+BD^2= AD^2\\ \\ x^2+[(1)/(2)(x+5)]^2= (x+5)^2\\ \\ x^2+ (1)/(4)(x+5)^2 = (x+5)^2\\ \\ 4x^2+(x+5)^2= 4(x+5)^2\\ \\ 4x^2= 3(x+5)^2\\ \\ 4x^2=3(x^2+10x+25)\\ \\ 4x^2-3x^2-30x-75=0\\ \\ x^2-30x-75=0

Using quadratic formula, we will get.......


x=(-(-30)\pm √((-30)^2-4(1)(-75)))/(2(1))\\ \\ x= (30\pm √(1200))/(2)\\ \\ x= 32.3205..., x=-2.3205...

(Negative value is ignored as the height of the pole can't be in negative)

So, the height of the flagpole will be:
32.3205... ft =(32.3205...* 12)inches = 387.846... \approx 388 inches

A flagpole is secured on opposite sides by two guy wires, each of which is 5 ft longer-example-1

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