# Two corners of a triangle have angles of # (7 pi )/ 12 # and # pi / 8 #. If one side of the triangle has a length of # 6 #, what is the longest possible perimeter of the triangle?

Perimeter # = a + b + c = 6 + 15.1445 + 12.4388 = 33.5833

Perimeter # = a + b + c = 6 + 15.1445 + 12.4388 =33.5833

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To find the longest possible perimeter of the triangle, use the law of sines to determine the lengths of the other two sides, then calculate the perimeter. The formula for the law of sines is:

( \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} )

Given angles: Angle A = ( \frac{7\pi}{12} ) Angle B = ( \frac{\pi}{8} )

Given side length: ( a = 6 )

Find the lengths of the other two sides:

For Angle A: ( \sin(\frac{7\pi}{12}) = \frac{a}{b} ) ( b = \frac{a}{\sin(\frac{7\pi}{12})} )

For Angle B: ( \sin(\frac{\pi}{8}) = \frac{a}{c} ) ( c = \frac{a}{\sin(\frac{\pi}{8})} )

Calculate the lengths: ( b = \frac{6}{\sin(\frac{7\pi}{12})} ) ( c = \frac{6}{\sin(\frac{\pi}{8})} )

Calculate the perimeter: ( \text{Perimeter} = a + b + c )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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