Question

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.

Answer 1

Answer:23 feet

Step-by-step explanation:

Answer 2

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