# A triangle has two corners with angles of # pi / 12 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?

Area of largest possible triangle

To get the largest possible are, smallest angle should correspond to the side of length 1.

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To find the largest possible area of the triangle given two angles and one side length, you can use the formula for the area of a triangle:

[ \text{Area} = \frac{1}{2} \times \text{side}^2 \times \frac{\sin(\text{angle}_1) \times \sin(\text{angle}_2)}{\sin(\text{angle}_1 + \text{angle}_2)} ]

Plugging in the given values: [ \text{side} = 1 ] [ \text{angle}_1 = \frac{\pi}{12} ] [ \text{angle}_2 = \frac{5\pi}{8} ]

[ \text{Area} = \frac{1}{2} \times 1^2 \times \frac{\sin\left(\frac{\pi}{12}\right) \times \sin\left(\frac{5\pi}{8}\right)}{\sin\left(\frac{\pi}{12} + \frac{5\pi}{8}\right)} ]

[ \text{Area} = \frac{1}{2} \times \frac{\sin\left(\frac{\pi}{12}\right) \times \sin\left(\frac{5\pi}{8}\right)}{\sin\left(\frac{17\pi}{24}\right)} ]

[ \text{Area} ≈ 0.35 ]

So, the largest possible area of the triangle is approximately ( 0.35 ) square units.

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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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