Two opposite sides of a parallelogram each have a length of #25 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #175 #, how long are the other two sides?

Answer 1

Other two sides are # 7.25# unit each .

Opposte sides of parallelogram is # s_1=25#

Angle of one corner of the parallelogram is

# /_theta = (5pi)/12=(5*180)/12=75^0# and
Area of parallelogram is # A_p=175 #
We know area of parallelogram is # A_p=s_1*s_2*sin theta # ,
where #s_2# is the adjacent side of sides #(s_1)#
#:. 175 =25*s_2*sin 75:. s_2= 175/(25*sin75) # or
#s_2= 175/(25*sin75) ~~ 7.25(2p)# unit
Other two sides are # 7.25(2p)# unit each . [Ans]
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Answer 2

Let's denote the length of one of the other two sides as ( a ) and the length of the other side as ( b ).

Given that the area of the parallelogram is ( 175 ), and we know the lengths of two adjacent sides are ( 25 ), we can use the formula for the area of a parallelogram: ( \text{Area} = \text{base} \times \text{height} ). Since the base (the side with length 25) is known, we can find the height.

The height of the parallelogram is the perpendicular distance between the side of length 25 and the opposite side. This height is also equal to the length of the other side of the parallelogram.

Now, we can use trigonometry to find the height. The given angle ( \frac{5\pi}{12} ) can help us find the height using trigonometric ratios.

Since the sine of an angle is opposite over hypotenuse, we have:

[ \sin\left(\frac{5\pi}{12}\right) = \frac{\text{height}}{25} ]

We can solve this equation to find the height, and then use the area formula to find the other two sides.

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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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