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A roof support with equally spaced vertical pieces is shown in below figure. Find the total length of the vertical pieces if the shortest one is 10.0 in




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The diagram points at a horizontal distance of 10.0 inches.  But it says vertical support is 10.0 inches.  I take it as the length (height) of shortest vertical support. See my diagram. There are totally 14 vertical supports.

Angle made by slanting support with horizontal = 90⁰ - 84.8⁰ = 5.2⁰

tan 5.2⁰ = 10.0" / a ,   where a is the distance from O to the shortest support.

a = 10.0" / tan 5.2⁰ = 109.88" 

tan 5.2⁰ = 10.0" / a = h / 224.0"

h = 224.0" * tan 5.2⁰ = 20.385 "  = height of longest vertical support.

Now the heights of the vertical supports are in arithmetic progression, as their lengths increase by fixed quantity = tan 5.2⁰ * horizontal spacing between them.

So sum of the heights of vertical supports = sum of arithmetic series
          = number of terms * ( first term + last term) / 2 
         = Number of vertical supports *
                    (height of smallest support + height of tallest support) / 2

        = 14 * ( 10" + 20.385")/2 = 212.695"

2 5 2
hope u understand it easily.
But the answer is 302.9 invhes
your diagram 10 inches is it horizontal or vertical distance? 224.0" is it from first support or from the vertex of triangle? clarify
there are 14 vertical supports. if there are 15 vertical supports, then ur answer may be correct. u need to chek what i asked and respond, then i will answer again. thanx
thanx n u r welcome
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