Question 1057675: You are told that a triangle has sides that are 7 inches and 4 inches long. You were also told that the sides form an angle that measure 53°. Is there only one triangle that has these given dimensions why or why not.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! We use the SAS formula. SAS stands for Side-Angle-Side:
c^2 = a^2+b^2-2ab cos(C)
where we have three sides, a, b, c, and c is our unknown side. C is the angle we know, it's opposite side c. Plug in the numbers:
c^2 = [(7^2+4^2)-2*7*4*cos(53)
c^2 = 49+16-56*0.602 = 31.288
sqrtc^2 = sqrt31.288
c = 6
There is only one triangle with sides 4, 6, 7 and angle C = 53°
:
John
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