MATH QUESTION!!

Question

A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 49 feet less than the height of the pole. If the wire is to be 14 feet longer than the height of the pole, what is the height of the pole?

Answer 1

Draw a figure where h is the height of the pole.

Then you should see that h² + (h-49)² = (h+14)² by the Pythagorean theorem.

Now solve for h.

Answer 2

1. First, draw a diagram of the situation. You'd have a right triangle with one leg of length h, to represent the pole, a hypotenuse (longest side) of h + 14, and the shortest leg with length h - 49.
2. Use the Pythagorean theorem (a² + b² = c²) to set up the equation h² + (h - 49)² = (h + 14)². (h + 14) is c in this equation because it is the length of the hypotenuse.
3. Expand the equation to get h² + (h² - 98h + 2401) = (h² + 28h + 196)
4. Subtract the right-hand side of the equation over to the left-hand side, giving you h² - 126h + 2205 = 0.
5. Use the quadratic formula, factoring, or a graph to solve for h. There are two positive values of h, which are 21 and 105. Only 105 is large enough to subtract 49, which is required for the distance between the bottom of the pole to the anchor point. So, this is the height of the pole, and the solution is 105 feet.