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

Question

agasfer [191]

2 years ago

12

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

ind the length of a diagonal.

Mathematics

2 answers:

Neko [114] · Answer 1 · 2022-06-04T13:22:05+03:00

Neko [114]2 years ago

8 0

Answer:23 feet

Step-by-step explanation:

snow_lady [41] · Answer 2 · 2022-06-04T12:01:45+03:00

snow_lady [41]2 years ago

3 0

Check the picture.

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:

$|DB|^{2}= |DA|^{2} + |DA|^{2} -2|DA|*|AB|*cos(DAB)$

$=9^{2}+23^{2}-2*9*2*(0.173)=81+529-6.228=603.7$

Thus, |DB|= $\sqrt{603.7}=24.6$ (ft)

Answer: 24.6 ft