Question

A metal frame is constructed in the form of an isosceles trapezoid. each base angle measures 80°, the length of the base is 7 feet, and each of the nonparallel sides is 5 feet long. determine the length of a diagonal brace to the nearest whole number. 5 ft 7 ft 8 ft 9 ft

Answer 1

1. Check the picture at the bottom.

2. ABCD is a right trapezoid so the diagonals have equal length. Lets find diagonal BD.

3. In triangle ABD we are given the length AB=7, AD=5 and m(A)=80°.

4. We use the cosine law: $BD^{2}=AB ^{2}+ AD^{2}-2AB*BD*cos(A)$

5. Cosine of 80 can be found with a scientific calculator or in the internet as cos80=0,17

6. $BD^{2}=7 ^{2}+ 5^{2}-2*7*5*0.17=49+25-11.9=62.1$

square root of BD=7.88, so the answer is 8 feet.