The bases of a trapezoid are 22 and 12 respectively. The angles at the extremities of one base are 65° and 40° respectively. Find the two legs.

2021-10-18
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The bases of a trapezoid are 22 and 12 respectively. The angles at the extremities of one base are 65° and 40° respectively. Find the two legs.

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Answered 2021-10-26 Author has 2252 answers

Construct the trapezoid ABCD ,where \(AB || CD\)
\(AB = 12\) and \(CD = 22\)
angle \(C=65^{\circ}\) and angle \(D = 40^{\circ}\)
Draw \(AE || BC\) where \(E\) is on \(CD\)
So now \(ABCE\) is a parallelogram, and \(CE = 12\)
which makes \(ED = 10\)
Now look at triangle \(AED,\) by corresponding angles
angle \(AED = 65°\), angle \(D = 40\) leaving angle \(DAE = 75°\)
by sine law:
\(\frac{AD}{\sin65} = \frac{10}{\sin75}\)


\(AD = \frac{10\sin65}{\sin75} = 9.38\)

by sine law:
\(AE \sin40 = {10}{\sin75}\)
\(AE = 6.65\)
but \(BC = AE\),
So the side adjacent to the \(65°\) angle is \(6.65\), the side adjacent to the \(40°\) angle is \(9.38\)

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