SOLUTION: Find the smallest angle, to the nearest degree in the triangle whose sides are, 5, 6 and 7.

Algebra ->  Trigonometry-basics -> SOLUTION: Find the smallest angle, to the nearest degree in the triangle whose sides are, 5, 6 and 7.       Log On


   

Question 783304: Find the smallest angle, to the nearest degree in the triangle whose sides are, 5, 6 and 7.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
The sides are a=5, b=6, c=7



The smallest angle is the one opposite the smallest side.

This is the case of SSS (side-side-side)

We use the law of cosines solved for the cosine:

cos(A) = %28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29

cos(A) = %286%5E2%2B7%5E2-5%5E2%29%2F%282%2A6%2A7%29

cos(A) = %2836%2B49-25%29%2F84

cos(A) = 60%2F84

cos(A) = 5%2F7

Use the inverse cosine on your calculator

A = 44.4153086°

A = 44° to the nearest degree.

Edwin