SOLUTION: Find the length of side x. Round to the nearest tenth. {{{drawing(400,160,-1.5,13,-1.5,4.3, locate(6,0,x), locate(7.3,2.9,114^o), locate(3.6,2.3,8.6), line(0,0,11.11075603,0), l

Algebra ->  Trigonometry-basics -> SOLUTION: Find the length of side x. Round to the nearest tenth. {{{drawing(400,160,-1.5,13,-1.5,4.3, locate(6,0,x), locate(7.3,2.9,114^o), locate(3.6,2.3,8.6), line(0,0,11.11075603,0), l      Log On


   

Question 1204459: Find the length of side x. Round to the nearest tenth.
Found 2 solutions by Theo, mccravyedwin:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you can use the law of sines to solve this.
the angle opposite 8.6 is equal to 180 minus (114 + 21) = 45 degrees.
8.6 is opposite 45 degrees.
x is opposite 114 degrees.
law of sines says 8.6 / sin(45) = x / sin(114).
solve for x to get x = 8.6 * sin(114) / sin(45) = 11.11075603.
round to 11.1.
that's your answer.
here's a reference on law of sines.
https://www.mathsisfun.com/algebra/trig-sine-law.html

Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!



For enrichment purposes, here's an alternate way to do the problem.  It's a
little longer, but you could do it this way if you forgot the law of sines.
Draw the altitude h from the vertex of the 114o angle. That splits the 114o angle
into the complement of 21o or 90o-21o=69o, and 114o-69o=45o. It also splits x, making

x = p+q.



Then using cosine = adjacent/hypotenuse in the rt. triangle on the left,
p%2F8.6=cos%2821%5Eo%29
p=8.6%2Acos%2821%5Eo%29
p=8.028791668

Then using sine = opposite/hypotenuse in the same rt. triangle,
h%2F8.6=sin%2821%5Eo%29
h=8.6%2Asin%2821%5Eo%29
h=3.081964366

Since the rt. triangle on the right has a 45o angle, it is 
isosceles, so q = h = 3.081964366.  Then

x = p + q = 8.028791668 + 3.081964366 = 11.11075603.

x rounds to 11.1

Edwin