# A triangle has two corners with angles of # pi / 2 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?

Largest possible area of the triangle is 1.2071

The remaining angle:

I am assuming that length AB (1) is opposite the smallest angle.

Using the ASA

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To find the largest possible area of the triangle, we can use the formula for the area of a triangle:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ]

Given that one side of the triangle has a length of 1, and the triangle has two angles of ( \frac{\pi}{2} ) and ( \frac{3\pi}{8} ), we can determine the height of the triangle using trigonometric functions.

Let's denote the angle ( \frac{3\pi}{8} ) as ( \theta ). Then, the height of the triangle can be calculated as:

[ \text{height} = \sin(\theta) \times \text{side} ]

After finding the height, we can use it to calculate the area of the triangle using the formula mentioned above. We'll maximize the area by maximizing the height, which occurs when ( \theta = \frac{3\pi}{8} ).

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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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