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A triangle has sides A, B, and C. The angle between sides A and B is #(7pi)/12# and the angle between sides B and C is #pi/12#. If side B has a length of 19, what is the area of the triangle?

Answer 1

Abigail Armstrong

#a = (1/2) a b sin C ~~ color(purple)(5.6783#

#hatC = (7pi)/12, hatA = pi/12, b = 19#

#hatB = pi - pi/12 - (7pi)/12 = pi/3#

#a / sin A = b / sin B#

#a = (1/2) a b sin C = (19 * sin (pi/12)) / sin(pi/3) ~~ color(purple)(5.6783#

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Answer 2

Carter Anderson

To find the area of the triangle given the lengths of its sides and the angles between them:

Use the Law of Cosines to find the length of side A.
Use the formula for the area of a triangle using side lengths and the included angle.
Calculate the area using Heron's formula, which requires knowing the lengths of all three sides of the triangle.

Following these steps, you can find the area of the triangle.

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Answer from HIX Tutor

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.