# A triangle has two corners with angles of # pi / 4 # and # pi / 4 #. If one side of the triangle has a length of #16 #, what is the largest possible area of the triangle?

128

Since our largest triangle has the largest area, we know that the first set is what we're looking for.

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The largest possible area of the triangle can be found using the formula for the area of a triangle given two sides and the angle between them. In this case, the two sides are equal (since the two angles are equal) and one side has a length of 16. Therefore, the other side also has a length of 16. Using the formula (Area = \frac{1}{2} \times \text{base} \times \text{height}), where the base is one of the sides and the height is the distance from the opposite corner to the base, we can calculate the area of the triangle. The height can be found using trigonometry, specifically the tangent function, since we know the angle and the adjacent side length.

(Area = \frac{1}{2} \times 16 \times 16 \times \tan(\frac{\pi}{4}))

(Area = \frac{1}{2} \times 16 \times 16 \times 1)

(Area = 128)

Therefore, the largest possible area of the triangle is 128 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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