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

Wednesday, December 31, 2014

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

We'll denote the measure of angle X as
m%28X%29

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

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

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

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

which leads to
p=856.9

p=856.9

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