Question

Advanced Trigonometry, pls help me answer this!​

Answer 1

Answer:   14.3 square cm

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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 = $\sin^{-1}$(0.535656) or A = 180-$\sin^{-1}$(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.