Question 849568: Solve the triangle(s): A= 30 degrees. a=2 square root 2 b=2+2 square root 3
Please help I have been stuck on this problem for 3 hours
Thanks in advance
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! since you know 2 of the sides, you can use the law of sines to find the other angle.
let's try that.
law of sines says that a/sinA = b/sinB = c/sinC
you have A = 30 and a = 2sqrt(2)
you have b = 2+2sqrt(3)
the ratio would be:
2sqrt(2) / sin(30) = 2+2sqrt(3)/sinB
cross multiply to get:
2sqrt(2) * sinB = sin(30) * (2+2sqrt(3))
divide both sides of this equation by 2sqrt(2) to get:
sinB = [(sin(30) * (2+2sqrt(3)] / 2sqrt(2)
since sin(30) is equal to 1/2, this formula becomes:
sinB = [(1/2) * (2 + 2sqrt(3)] / 2sqrt(2)
at this point in time I went to my calculator to find that:
sinB = .9659258263 from where i found that B = 75 degrees.
since B = 75 degrees, and A = 30 degrees, and the sum of the angle of a triangle is equal to 180 degrees, then angle C must be equal to 180 - 75 - 30 which is equal to another 75 degrees.
75 + 75 + 30 = 180 so that check out ok.
if that's the case, then the side opposite angle C, which is side c, must also be equal to 2 + 2sqrt(3).
you have all the sides and all the angles so I think your answer must be in there somewhere.
This is an isosceles triangle because 2 of the angles and 2 of the sides are equal.
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