Question

A flagpole is secured on opposite sides by two guy wires, each of which is 6 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)?

Answer 1

Let x be the height of the pole.

The flagpole and the guy wires form a triangle with two sides of x+6.

The bottom/third side is also x+6.

So we have an equalateral triangle with sides x+6. The flagpole is perpendicular to the third side so bisects the triangle into two right triangles and the base into two equal parts of length (x+6)/2.

Since each half is a right triangle we have:

((x+6)/2)^2 + x^2 = (x+6)^2

Expand this and solve for x.