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

The solution is 11 feet

Step-by-step explanation:

We know that this footbridge has two right triangles that support the bridge, meeting at the center. The triangles will by congruent by AAS, provided we know that each of the triangles are 90 - 65 - 25, and that the hypotenuse of each triangle has a common length of x.

Let us say the side opposite to the 25 degree angle is a, in both triangles. The side opposite to the 65 degree angle is b, but we already know the length of b as it is 20 / 2 = 10 ft. We should find the length of a by tan 25, and, by Pythagorean Theorem, determine the length of x.

a = tan 25 * ( 10 ) ≈ 4.663 ft

b = 10 ft

By Pythagorean Theorem,

a^2 + b^2 = x^2,

( 4.663 )^2 + ( 10 )^2 = x^2,

21.74 + 100 = x^2,

x^2 = 121.74,

x  ≈ 11 ft ( to the nearest foot )

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