Question

An inpector Needs to find the dimensions of a Roof truss. the length of a bottom truss is 2.5 times the height of the truss. The length of the top chord is 21 feet, Which includes a 5 foot overhang. The bottom cord and the king's post are perpendicular. What are the names of the bottom chord and king's post. Round your answer to the nearest foot.​

Answer 1

• bottom chord: 25 ft
• king post: 10 ft

Explanation:

You want the lengths of the bottom chord and king post if the ratio of their lengths is 2.5:1 and the length of the top chord, including a 5 ft overhang, is 21 ft.

Pythagorean theorem

The distance AB in the diagram will be the top chord length less the overhang, or ...

AB = 21 ft -5 ft = 16 ft

If BC in the diagram is represented by h, then AC = 2.5h. The length of AD is half that, of 1.25h.

The Pythagorean relation tells us ...

AB² = AD² +BD²

16² = h² +(1.25h)²

256 = 2.5625h²

h = √(256/2.5625) ≈ √99.9024 ≈ 9.995 ≈ 10

Then AC = 2.5h = 2.5×10 = 25

The bottom chord is 25 ft and the king post is 10 ft.

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