# geometry

The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°.

a.
Find the length of the diagonal.
b.
Find the length of the shorter base.

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1. Drop altitudes of length a from the ends of the shorter base. This gives you two right triangles at the ends, with altitude a and base x. Since the figure is isosceles, the two base angles are equal.

Now you have
Each base angle is 70°

a/7 = cos70°
x^2 + a^2 = 7^2

Now you know that if the shorter base is b,
2x+b = 22

the diagonal d is thus
d^2 = (x+b)^2 + a^2

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