A parallelogram has two adjacent sides of 10 cm and 15 cm. It also has an angle of 75°. What is the length of the shorter diagonal?

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Answer 1 · 2018-01-17T11:45:22

Length of shorter diagonal is #15.73# unit.

The adjacent sides of the parallelogram are #s_1=10 # cm and

#s_2=15# cm and corner angle #theta_1=75^0#

Consecutive angles are supplementary

#:.theta_2=180-75=105^0#.

Shorter diagonal can be found by applying cosine law:

#d_s= sqrt(s_1^2+s_2^2-2*s_1*s_1*costheta_1)#

#=sqrt(10^2+15^2-2*10*15*cos75) ~~15.73# unit

Length of shorter diagonal is #15.73# unit [Ans]

[Ans]