Problema Solution
If the sides of a parallelogram and an included angle are 6, 10 and 100 degrees respectively, find the length of the shorter diagonal
Answer provided by our tutors
Let
a = 10
b = 6
the angle B = 100
d = the shorter diagonal
Angle A + Angle B = 180
Angle A = 180 - Angle B
Angle A = 180 - 100
Angle A = 80
Using the The Law of Cosines we have
d^2 = a^2 + b^2 - 2ab cos(Angle A)
d^2 = 6^2 + 10^2 - 2*6*10*(cos(80))
by solving we find
d = 10.73
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The length of the shorter diagonal is 10.73.