A triangle has two corners with angles of # pi / 4 # and # pi / 4 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?

Answer 1

Largest possible area of the triangle #Delta ABC = (1/2) * 1 * 1 = color (green)(0.5)# sq. units

Three angles are #pi/4, pi/4, (pi-(pi/4 + pi/4)) = pi/2#

It’s an isosceles right triangle with sides in the ratio #1 : 1 : sqrt2#

To get the largest possible area of the triangle, length ‘1’ should correspond to the smallest angle, viz. #pi/4#

Hence the sides are #1, 1, sqrt2#

Largest possible area of the triangle #Delta ABC = (1/2) * 1 * 1 = color (green)(0.5)# sq. units

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Answer 2

To find the largest possible area of the triangle given two angles of (\frac{\pi}{4}) each and one side length of (1), follow these steps:

  1. Since two angles are equal, it implies that the triangle is an isosceles triangle.

  2. To maximize the area of the triangle, make the non-common side the base of the triangle.

  3. Construct the altitude from the vertex opposite the base to the midpoint of the base, creating two right triangles.

  4. Since the triangle is isosceles, the altitude will bisect the base, resulting in two right triangles with base and height of (\frac{1}{2}).

  5. Use the formula for the area of a triangle: (\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}), where the base is (1) and the height is (\frac{1}{2}) for each right triangle.

  6. Calculate the area of one right triangle, then double it to get the total area of the isosceles triangle.

By following these steps, you will find the largest possible area of the triangle.

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Answer from HIX Tutor

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.

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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