A triangle has a=80 inches and b=100 inches. If the measure of angle A is 135, what is the length of c to the nearest inch?

Question

Please show the steps to get the answer.

The following choices were provided for answers:

A.) 23 inches

B.) 32 inches

C.) 128 inches

D.) None of the above

Answer 1

if we assume that ∠A is formed by the two sides whose lengths are given, then we can use the side-angle-side property

to solve this problem; by inspection, we see that answers A and B can not be correct because angle A creates an obtuse triangle, and the length of the missing side must be greater than either existing side.

 

To find the length of the missing side, we can use the law of cosines:   c² = a² + b² − (2bc cosA)

 

in this case, the length is 179.8

 

so, the problem answer is D