SOLUTION: 1.The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59 degree. Find the length of side AC.

Algebra ->  Triangles -> SOLUTION: 1.The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59 degree. Find the length of side AC.      Log On


   

Question 1039429: 1.The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59 degree. Find the length of side AC.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the law of sines to find angle A.
sin%2859%29%2F12=sin%28A%29%2F8
sin%28A%29=%288%2F12%29sin%2859%29
sin%28A%29=%283%2F4%29%280.8572%29
A=40deg
and
A%2BB%2BC=180
40%2BB%2B59=180
B=81
Then using the law of sines again,
sin%2859%29%2F12=sin%2881%29%2FAC
AC=12%2A%28sin%2859%29%2Fsin%2881%29%29
A=12%280.8679%29
A=10.4