Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #36 #, how long are the other two sides?

Answer 1

The other two sides are 2.3095 long each

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Answer 2

Let the other two sides of the parallelogram be (a) and (b). The area of a parallelogram can be calculated using the formula:

[ \text{Area} = \text{base} \times \text{height} ]

Given that one side of the parallelogram is 8 and the adjacent angle is (\frac{\pi}{3}), the height can be found using trigonometry. Since the opposite side of the angle (\frac{\pi}{3}) is 8, we can use the sine function to find the height:

[ \sin\left(\frac{\pi}{3}\right) = \frac{\text{height}}{8} ]

[ \text{height} = 8 \times \sin\left(\frac{\pi}{3}\right) = 8 \times \frac{\sqrt{3}}{2} = 4\sqrt{3} ]

Given that the area of the parallelogram is 36, and the height is (4\sqrt{3}), we can find the length of the other base ((b)) using the formula:

[ 36 = 8 \times b ]

[ b = \frac{36}{8} = 4.5 ]

Thus, the lengths of the other two sides are (a = 8) and (b = 4.5).

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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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