A trapezoid

A trapezoid with a base length of a = 36.6 cm, with angles α = 60°, β = 48° and the height of the trapezoid is 20 cm. Calculate the lengths of the other sides of the trapezoid.

Correct answer:

b =  23.094 cm
d =  26.9127 cm
c =  5.1356 cm

Step-by-step explanation:

a=36.6 cm α=60 β=48  h=20 cm  sinα=h:b  b=h/sin(α)=20/sin(60)=23.094 cm
sinβ=h:d  d=h/sin(β)=20/sin(48)=26.9127 cm
x1+c+x2=a cosα=x1:d=x1:26.9127=0 cosβ=x2:d=x2:26.9127=0  c=ad (cosα+cosβ)=ad (cos60 +cos48 )=36.626.9127 (cos60 +cos48 )=36.626.9127 (0.5+0.669131)=5.136=5.1356 cm

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