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?

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.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x