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morgan4411
20.09.2019 •
Mathematics
Ametal 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
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Ответ:
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)](/tpl/images/0246/1380/946bf.png)
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](/tpl/images/0246/1380/65993.png)
square root of BD=7.88, so the answer is 8 feet.
Ответ: