Question 849568
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.