Question
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.
a.
Find the length of the diagonal.
b.
Find the length of the shorter base.
Round your answers to the nearest hundredth.
Answers
Steve
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
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