Question

A pole 5 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, Zachary 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.

Answer 1

The length of the guy's wire to the nearest foot is 89 feet.

The situation forms a right-angled triangle.

Properties of a right angle triangle:

• A right-angle triangle has one angle of 90 degrees.
• The sides can be found using the Pythagoras theorem.
• The angles can be found using trigonometric ratios.

The hypotenuse of the triangle is the length of the wire.

let's use the smaller triangle to find the angle opposite the tower. Therefore,

tan ∅ = opposite / adjacent

tan ∅ =  5 / 2

∅ = tan⁻¹ 2.5

∅ = 68.1985905136

∅ = 68.20°

Therefore,

cos 68.20 = adjacent / hypotenuse

cos 68.20 = 33 / hypotenuse

hypotenuse = 33 / cos 68.20

hypotenuse = 88.8606843161

Therefore,

length of wire ≈ 89 feet.

learn more on triangles here; brainly.com/question/25762788?referrer=searchResults