Question

A 20
-foot-long footbridge has two diagonal supports that meet in the center of the bridge.

Each support makes a 65
angle with a short vertical support.

A diagram shows the footbridge, the diagonal supports and the vertical supports create two right triangles. At the top of the diagram a horizontal line is shown and labeled 20 feet. The two right triangles are shown below this horizontal line.The two longest legs of both right triangles touch at the center of the footbridge.The shortest leg of both right triangles represents the vertical support on each end of the footbridge. The hypotenuse of both right triangles form the diagonal supports that meet at the center of the footbridge. The full length of the footbridge is 20 feet. The vertical supports are not labeled. Each diagonal support is labeled X. A 65-degree-angle is formed between the short vertical support and the diagonal support on each end of the bridge.

What is the length x of a diagonal support, to the nearest tenth of a foot?

Answer 1

Each diagonal forms a right triangle with half the bridge as the horizontal leg: half of 20 ft is 10 ft. The angle between the vertical leg and the diagonal is 65°, so the acute angle at the base is 25° (since 90° − 65° = 25°).

Using cosine for the 25° angle:
cos 25° = adjacent/hypotenuse = 10/x → x = 10 / cos 25° ≈ 10 / 0.9063 ≈ 11.0 ft.

So each diagonal support is about 11.0 feet long.