Answer: 14.3 square cm
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Step-by-step explanation:
We have this given info
- side a = 5
- side c = 6
- angle C = 40
Let's apply the law of sines to find angle A
sin(A)/a = sin(C)/c
sin(A)/5 = sin(40)/6
sin(A) = 5*sin(40)/6
sin(A) = 0.535656
A =
(0.535656) or A = 180-
(0.535656)
A = 32.388411 or A = 147.611589
There are two possibilities here we need to check.
If you were to try A = 147.611589 along with C = 40, then A+B+C = 180 solves to B = -7.6116 approximately. This isn't valid because the angles cannot be negative. So we rule out the case that A = 147.611589
If we tried A = 32.388411 and C = 40, then we'd get B = 107.611589 which is a valid angle.
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The last step is to use the SAS triangle area formula to get...
area = 0.5*side1*side2*sin(angle)
area = 0.5*a*c*sin(B)
area = 0.5*5*6*sin(107.611589)
area = 14.296942
This rounds to 14.3 when rounding to 3 significant figures.