Question

A pole 10 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Makayla measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

i dont know the ft of the tower but the pole is 10ft and at the bottem its labled how far the wire had to go from the groud to the pole its 2ft and from the pole to the tower its 9ft meaning from the ground to the tower it would be 11ft

Answer 1

Draw a straight line from the top of the tower (height H) down to the stake 11 ft away (9 ft from tower to pole + 2 ft from pole to stake). At the pole (9 ft from the tower) the wire is 10 ft above the ground, so the height at x = 9 is 10.

Because the wire is a straight line, heights scale linearly:
y(9) = H*(1 - 9/11) = H*(2/11) = 10, so H = 10 * 11/2 = 55 ft.

The wire runs from (0,55) to (11,0), so its length is
sqrt(11^2 + 55^2) = sqrt(3146) ≈ 56.1 ft.

To the nearest foot the guy wire is 56 ft.