# A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #4#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?

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To find the length of side (C) in the triangle given sides (A) and (B) and the angle between them, you can use the Law of Cosines, which states:

[C^2 = A^2 + B^2 - 2AB\cos(\theta)]

Where:

- (C) is the length of the side opposite the given angle.
- (A) and (B) are the lengths of the other two sides.
- (\theta) is the measure of the angle between sides (A) and (B).

Given that (A = 7), (B = 4), and (\theta = \frac{\pi}{6}), we can plug these values into the formula:

[C^2 = 7^2 + 4^2 - 2 \times 7 \times 4 \times \cos\left(\frac{\pi}{6}\right)]

[C^2 = 49 + 16 - 56 \times \frac{\sqrt{3}}{2}]

[C^2 = 65 - 28\sqrt{3}]

Taking the square root of both sides:

[C = \sqrt{65 - 28\sqrt{3}}]

This is the exact length of side (C). If you want a decimal approximation, you can calculate it further.

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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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