Question

a vertica tv atenna sits on the roof. two 78 foot guy wires are positioned on opposite sides of the atteena. the angle of elevation each makes with the ground is 23 degrees. How far apart are the ends of the two guy wires

Answer 1

Let the antenna base be the vertex. Each 78-ft guy wire makes a 23° angle with the ground, so the horizontal distance from the base to one anchor is 78 cos(23°). The anchors are on opposite sides, so the distance between them is

2 × 78 cos(23°) = 156 cos(23°) ≈ 143.6 ft.

(About 144 feet.)