SOLUTION: The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the side opposite the smallest angle of the triangle is

Algebra ->  Triangles -> SOLUTION: The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the side opposite the smallest angle of the triangle is       Log On


   

Question 1038316: The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the side opposite the smallest angle of the triangle is __?__ centimeters.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
11x%2B5x%2B2x=180
18x=180
x=10

Smallest angle of 20 degrees is opposite of the smallest side.
Largest angle of 110 degrees is opposite of the largest side of 5.5 centimeters.


Let s be the length of the smallest side.
sin%28110%29%2F5.5=sin%2820%29%2Fs

s%2F%28sin%2820%29%29=5.5%2Fsin%28110%29

s=5.5%28sin%2820%29%29%2F%28sin%28110%29%29