SOLUTION: Two angles in a triangle are 49 and 61. If the longest side of the triangle is 15 cm longer than the shortest side, what are the lengths of all three sides of the triangle?

Algebra ->  Triangles -> SOLUTION: Two angles in a triangle are 49 and 61. If the longest side of the triangle is 15 cm longer than the shortest side, what are the lengths of all three sides of the triangle?      Log On


   

Question 960463: Two angles in a triangle are 49 and 61. If the longest side of the triangle is 15 cm longer than the shortest side, what are the lengths of all three sides of the triangle?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The other angle is,
180-49-61=70
A=49
B=61
C=70
a=S
c=15%2BS
Use the law of sines,
sin%28A%29%2Fa=sin%28C%29%2Fc
sin%2849%29%2FS=sin%2870%29%2F%28S%2B15%29
%28S%2B15%29sin%2849%29=Ssin%2870%29
Ssin%2849%29-Ssin%2870%29=-15sin%2849%29
S%28sin%2849%29-sin%2870%29%29=-15sin%2849%29
S=%2815sin%2849%29%29%2F%28sin%2870%29-sin%2849%29%29
S=61.2
S%2B15=76.2
And,
sin%2861%29%2Fb=sin%2849%29%2F61.2
bsin%2849%29=61.2sin%2861%29
b=61.2%28sin%2861%29%2Fsin%2849%29%29
b=70.9