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.

Round your answers to the nearest hundredth.

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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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