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) Use the Law of Cosines to find the length of the diagonal.
A) Use the Law of Sines to find the length of the shorter base.
Round your answers to the nearest hundredth.

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Answer 1

The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

How to determine the length

The cosine rule is given as;

$c = \sqrt{a^2 + b^2 - 2ab cos \alpha }$

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

$c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}$

$c = \sqrt{533 - 308 * 0. 7660}$

$c = \sqrt{533 - 235. 93}$

$c = \sqrt{297. 072}$

$c = 17. 24$ feet

Using sine rule

$\frac{a}{sin A } = \frac{c}{sin C}$

$\frac{a}{sin 70} = \frac{17. 24}{sin 40}$

Cross multiply

$a$ × $sin 60$ = $c$ × $sin 70$

$a$ × $0. 8660$ = $17. 24$ × $0. 9397$

$a = \frac{16. 20}{0. 8660}$

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

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