The longer base of an isosceles trapezoid measures 23 ft. The nonparallel sides measure 9 ft, and the base angles measure 80°. Find the length of a diagonal.

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Consider the triangle DAB, with |DA|=9 ft, |AB|=23 ft and m(DAB)=80°.

To find the length of the diagonal, |DB|, we use the cosine law:

[tex]|DB|^{2}= |DA|^{2} + |DA|^{2} -2|DA|*|AB|*cos(DAB)[/tex]

[tex]=9^{2}+23^{2}-2*9*2*(0.173)=81+529-6.228=603.7[/tex]

Thus, |DB|= [tex] \sqrt{603.7}=24.6[/tex] (ft)

Answer: 24.6 ft

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2022-08-10T11:39:31+02:00

The length of a diagonal DA will be equal to 24.6 ft.

What is an isosceles trapezoid?

An isosceles trapezoid is a convex quadrilateral with one set of opposite sides divided by a line of symmetry. It is an uncommon instance of a trapezoid. Alternately, it can be described as a trapezoid with equal amounts of both the base angles and the legs.

It is given that the longer base of an isosceles trapezoid measures 23 ft. The nonparallel sides measure 9 ft, and the base angles measure 80°.

The image of an isosceles trapezoid is attached with the answer below. The diagonal will be calculated as below:-

Consider the triangle DAB, with |DA|=9 ft, |AB|=23 ft, and m(DAB)=80°. To find the length of the diagonal, |DB|, we use the cosine law:

DB² = DA² + AB² - 2(DA)(AB) x cos(DAB)

DB² = 9² + 23² - ( 2 x 9 x 2 x 0.173)

DB² = 81 + 529 - 6.22

DB² = 603.7

DB = √603.7

DB = 24.6 ft

Therefore, the length of a diagonal DA will be equal to 24.6 ft.

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