SOLUTION: In Δ​XYZ, angle∠Y=79​, X=10​, and X=12. To the nearest​ tenth, what is mangle∠​Z?

Algebra ->  Triangles -> SOLUTION: In Δ​XYZ, angle∠Y=79​, X=10​, and X=12. To the nearest​ tenth, what is mangle∠​Z?       Log On


   

Question 1072172: In Δ​XYZ, angle∠Y=79​, X=10​, and X=12. To the nearest​ tenth, what is mangle∠​Z?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean Y=12.
So use the law of sines to find angle X.
sin%28Y%29%2Fy=sin%28X%29%2Fx
sin%2879%29%2F12=sin%28X%29%2F10
sin%28X%29=%2810%2F12%29sin%2879%29
sin%28X%29=0.8180
X=54.9
So then you know,
X%2BY%2BZ=180
54.9%2B79%2BZ=180
Z=46.1