Question

A 15 ft long cable is connected from a hook to the top of a pole that has an unknown height. The distance from the hook to the base of the pole is 3 ft shorter than the height of the pole.

a. What can you use to find the height of the pole?
b. Write and solve a quadratic equation to find the height of the pole.
c. How far is the hook from the base of the pole?

Answer 1

a. What can you use to find the height of the pole?

solution: We can use Pythagoras theorem to find the height of the pole.

b. Write and solve a quadratic equation to find the height of the pole.

solution:

a² + b² = c²

`\sf (x)^2 + (x-3)^2 = 15^2`

`\sf x^2 + x^2 - 6x + 9 = 15^2`

`\sf 2x^2 -6x + 9 = 225`

`\sf 2x^2 -6x -216=0`

`\sf 2x^2 -24x +18x -216 = 0`

`\sf 2x(x-12)+18(x-12) = 0`

`\sf (2x + 18)(x-12) = 0`

`\sf x = 12, -9`

`\sf x = 12`

height of the pole: 12 ft

c. How far is the hook from the base of the pole?

solution: (x-3) → (12-3) → 9