SOLUTION: In OPQ, o = 870 inches, P = 80 degrees, and Q = 9 degrees. Find the length of p to the nearest 10th of an inch.

Algebra ->  Triangles -> SOLUTION: In OPQ, o = 870 inches, P = 80 degrees, and Q = 9 degrees. Find the length of p to the nearest 10th of an inch.      Log On


   

Question 935669: In OPQ, o = 870 inches, P = 80 degrees, and Q = 9 degrees. Find the length of p to the nearest 10th of an inch.
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
We'll denote the measure of angle X as
m%28X%29
In any triangle the sum of the angles is 180 degrees, so
m%28P%29%2Bm%28Q%29%2Bm%28O%29=180
so we know
m%28O%29=180-%28m%28P%29%2Bm%28Q%29%29=180-89=91
Now using the Law of Sines we write:

%0D%0Ap%2Fsin%2880%29=%28870%29%2F%28sin%2891%29%29%0D%0A

which leads to
p=856.9