Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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 51 feet less than the height of the pole. If the wire is to be 24 feet longer than the height of the pole, what is the height of the pole?

Sagot :

mberisso

Answer:

Height is 135 ft

Step-by-step explanation:

Notice that wire, pole, and ground form a right angle triangle, for which we name h = height of the pole one of the legs (the horizontal leg) is h - 51. The wire (which is the hypotenuse of the right angle triangle is: h + 24.

Then we can use the Pythagorean theorem to solve for the height (h):

h^2 + (h - 51)^2 = (h + 24)^2

h^2 + h^2 -102 h + 2601 = h^2 + 48 h + 576

grouping all terms on the left of the equal sign, we get:

h^2 -150 h + 2025 = 0

This gives two possible answers:

h = 135

and

h = 15

We opt for h = 135, because the other solution will render a negative leg for the triangle.

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.