Answer:
Length of the longer diagonal is 53 feet.
Step-by-step explanation:
We are given that,
Dimensions of the parallelogram is 40 feet and 20 feet and the smaller angle is 60°.
Let, the length of the diagonal be 'x' feet.
As the smaller angle is 60°, then the larger angle will be [tex]\frac{360-2(60)}{2}[/tex] = [tex]\frac{360-120}{2}[/tex] = [tex]\frac{240}{2}[/tex] = 120°
Using the Law of Cosines for the triangle made by the diagonal, we have,
[tex]x^{2}=20^{2}+40^{2}-2\times 20\times 40\times \cos120[/tex]
i.e. [tex]x^{2}=400+1600-1600\times (-0.5)[/tex]
i.e. [tex]x^{2}=2000+800[/tex]
i.e. [tex]x^{2}=2800[/tex]
i.e. x= 53 feet
Thus, the length of the longer diagonal is 53 feet.
