The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. Th

Question

4 years ago

14

The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. Th

e 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. show work please!

Mathematics

1 answer:

swat32 · Answer 1 · 2022-01-06T05:44:08+03:00

Answer:

Step-by-step explanation:

<h2>as the non parallel sides are equal and it is a trapezoid.</h2><h2>∴ base angles are equal.</h2><h2>each base angle=1/2×140=70°</h2><h2>let the foot of perpendicular from end of shorter side is at distance x from nearest end of longer side.</h2><h2> $\frac{x}{7}=cos ~70\\x=7 \times cos~70 \approx 2.394\\2x \approx 4.788 \approx 4.79\\$ </h2><h2>shorter side=22-4.79=17.21 ft</h2><h2>to find diagonal use cos formula</h2><h2> $cos ~70=\frac{22^2+7^2-d^2}{2*22*7} \\308 cos~70=484+49-d^2\\d=\sqrt{533-308~cos~70} \approx~20.68\\where ~d~is~diagonal.$ </h2><h2>d=20.68 ft</h2>