Answer:
4.2 feet
Explanation:
You want the altitude of a right triangle to its hypotenuse of length 14.3 ft when the legs are given as 13.6 ft and 4.4 ft.
Area
The area of a triangle is the same regardless of how it is computed. Using the legs of the triangle, we find it to be ...
A = 1/2bh = 1/2(13.6 ft)(4.4 ft) = 29.92 ft²
Using the hypotenuse and the unknown support length (x), it is ...
A = 1/2bh = 1/2(14.3 ft)(x ft) = 7.15x ft²
Equating these area values, we have ...
7.15x = 29.92
x = 29.92/7.15 ≈ 4.1846 ≈ 4.2 . . . . . feet
The support needs to be about 4.2 feet long.
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Alternate solution
The triangles in this diagram are similar, so the ratio of long side to hypotenuse of each is the same:
x/4.4 = 13.6/14.3
x = (4.4·13.6)/14.3 . . . . same as above, but without the factors of 1/2