# 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
Hello everyone! I'm a college student and taking a couse of Electrical Engineering. I hope you will help me with my homework. Thank you!

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

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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 $$9.38$$