The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
The cosine rule is given as;
[tex]c = \sqrt{a^2 + b^2 - 2ab cos \alpha }[/tex]
c = length of the diagonal
a = base length = 22 feet
b = 7 feet
[tex]c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}[/tex]
[tex]c = \sqrt{533 - 308 * 0. 7660}[/tex]
[tex]c = \sqrt{533 - 235. 93}[/tex]
[tex]c = \sqrt{297. 072}[/tex]
[tex]c = 17. 24[/tex] feet
Using sine rule
[tex]\frac{a}{sin A } = \frac{c}{sin C}[/tex]
[tex]\frac{a}{sin 70} = \frac{17. 24}{sin 40}[/tex]
Cross multiply
[tex]a[/tex] × [tex]sin 60[/tex] = [tex]c[/tex] × [tex]sin 70[/tex]
[tex]a[/tex] × [tex]0. 8660[/tex] = [tex]17. 24[/tex] × [tex]0. 9397[/tex]
[tex]a = \frac{16. 20}{0. 8660}[/tex]
a = 18. 7 feet long
Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
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