A triangle has two corners with angles of # ( pi ) / 2 # and # ( pi )/ 6 #. If one side of the triangle has a length of #4 #, what is the largest possible area of the triangle?

Answer 1

Largest possible area of the right #Delta ABC = color(green)(~~ 13.8564)# sq units

Three angles are #A = pi/2, B = pi/6, C = pi/3#

It is a right triangle with angles 30, 60, 90 and the sides will be in

the ratio of 1 : #sqrt3 # : 2

To get the largest are, side 4 should correspond to the least angle #pi/6#

Three sides will be #4, 4sqrt3, 8#

Largest possible area of the right #Delta ABC = (1/2) * 4 * 4sqrt3 color(green)(~~ 13.8564)# sq units

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Answer 2

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

Area = 1/2 * base * height

Since we know one side of the triangle is 4 units long, let's call this side the base. The height of the triangle will be the distance from the opposite vertex (the one not on the 4-unit side) to the base.

To find the height, we can use trigonometry. Since we know the angles of the triangle are π/2 and π/6, we can find the height using the sine of π/6.

sin(π/6) = opposite/hypotenuse

We can rearrange this to find the height:

height = sin(π/6) * hypotenuse

Since the hypotenuse of the right triangle formed by the height is the side opposite to the right angle (which is the base, 4 units), the hypotenuse is also 4 units.

So, height = sin(π/6) * 4

Now, we can plug the values of base and height into the formula for the area of a triangle:

Area = 1/2 * 4 * sin(π/6) * 4

Area = 1/2 * 4 * (1/2) * 4

Area = 8

Therefore, the largest possible area of the triangle is 8 square units.

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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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