# Two corners of a triangle have angles of # ( pi )/ 3 # and # ( pi ) / 6 #. If one side of the triangle has a length of # 5 #, what is the longest possible perimeter of the triangle?

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To find the longest possible perimeter of the triangle given two angles and one side length:

- Determine the measure of the third angle by subtracting the sum of the given angles from ( \pi ).
- Use the Law of Sines to find the lengths of the other two sides.
- Calculate the perimeter by adding the lengths of all three sides.
- Choose the maximum value for the perimeter.

The longest possible perimeter of the triangle will be obtained when the third angle is as small as possible, making the triangle as close to equilateral as possible. Therefore, the third angle will be ( \frac{\pi}{2} ). Then apply the Law of Sines to find the lengths of the other two sides, and calculate the perimeter using the given side length.

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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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- A chord with a length of #5 # runs from #pi/8 # to #pi/3 # radians on a circle. What is the area of the circle?
- What is the volume of a sphere if the radius is 28cm?

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