# Two corners of a triangle have angles of #(3 pi ) / 4 # and # pi / 6 #. If one side of the triangle has a length of #9 #, what is the longest possible perimeter of the triangle?

Longest Possible perimeter is

Now, let's say

Using Sine Rule we have,

Using above set of equations, we have the following:

Now, to find the longest possible perimeter of the triangle

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The longest possible perimeter of the triangle is (18 + 9\sqrt{3})

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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.

- Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 12 #. If one side of the triangle has a length of # 3 #, what is the longest possible perimeter of the triangle?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #42 # and the height of the cylinder is #1 #. If the volume of the solid is #480 pi#, what is the area of the base of the cylinder?
- A rectangular box has the dimensions #12\times 18 \times 14# inches. What's its volume? What's its surface area?
- A chord with a length of #5 # runs from #pi/8 # to #pi/2 # radians on a circle. What is the area of the circle?
- Two corners of a triangle have angles of # (3 pi )/ 8 # and # ( pi ) / 2 #. If one side of the triangle has a length of # 7 #, what is the longest possible perimeter of the triangle?

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