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.A. 17 ftB. 25 ftC. 23 ftD. 20 ft

Answer 1

The diagram below represent the information given in the question

From the diagram

`\begin{gathered} AD=9ft \\ DC=23ft \\ <\text{ADC}=80^0 \\ AC=d=\text{diagonal} \end{gathered}`

The diagonal of the trapezoid can be calculated using cosine rule as shown below:

`d^2=AD^2+DC^2-2* AD* DC*\cos D`

`d^2=9^2+23^2-2*9*23*\cos 80^0`
`\begin{gathered} d^2=81+529-414*0.1736 \\ d^2=610-71.80 \\ d^2=538.10965 \end{gathered}`
`\begin{gathered} d=\sqrt[]{538.10965} \\ d=23.197 \\ d\approx23ft \end{gathered}`

Hence, the length of the diagonal is 23ft, OPTION C