A -foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a angle with a short vertical support.

Complete question :

A 25-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.

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

Answer:

13.80 feets

Step-by-step explanation:

Taking either of the triangles formed and attached to the picture, the length of diagonal, x can be obtained using Pythagoras rule :

To obtain x :

Sinθ = opposite / hypotenus

Opposite = 12.5 feets ; hypotenus = x ; θ = 65°

Sin 65 = 12.5 / x

0.9063077 * x = 12.5

x = 12.5 / 0.9063077

x = 13.792225

x = 13.80 feets

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