# A triangle has sides A, B, and C. If the angle between sides A and B is #(pi)/3#, the angle between sides B and C is #(5pi)/12#, and the length of B is 2, what is the area of the triangle?

Area of triangle

Area of triangle

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The area of the triangle can be calculated using Heron's formula, which states that the area (A) of a triangle with side lengths (a), (b), and (c) is given by:

[A = \sqrt{s(s - a)(s - b)(s - c)}]

Where (s) is the semi-perimeter of the triangle, calculated as:

[s = \frac{a + b + c}{2}]

Given that side (b) is 2 units, and the angles between sides (a) and (b) and between sides (b) and (c) are ( \frac{\pi}{3} ) and ( \frac{5\pi}{12} ) respectively, we can use the law of cosines to find the lengths of sides (a) and (c). Then, we can calculate the semi-perimeter and finally the area of the triangle using Heron's formula.

Using the law of cosines, we have:

[c^2 = a^2 + b^2 - 2ab \cdot \cos(\frac{5\pi}{12})]

[a^2 = b^2 + c^2 - 2bc \cdot \cos(\frac{\pi}{3})]

After calculating (a) and (c), we can find the semi-perimeter (s) and then use Heron's formula to find the area of the triangle.

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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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