Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(11 pi)/12 # and the parallelogram's area is #48 #, how long are the other two sides?

Answer 1

#=46.36#

Area#=ab sin theta# where #a=4;theta=11pi/12 and Area =48# We have to find #b=?# So #4b sin(11pi/12)=48# or #b(0.2588)=48/4# or #b=12/0.2588# or #b=46.36#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Given that the length of two opposite sides of the parallelogram is 4 and the area of the parallelogram is 48, we can use the formula for the area of a parallelogram:

Area = base × height

Since two opposite sides are given as 4, we can consider one of these sides as the base. Let's denote the other side (the height) as h.

So, we have:

48 = 4 × h

Solving for h, we get:

h = 48 ÷ 4 = 12

Now, to find the length of the other two sides, we need to use the given angle of ( \frac{11\pi}{12} ).

In a parallelogram, opposite angles are equal. So, if one angle is ( \frac{11\pi}{12} ), then the opposite angle is also ( \frac{11\pi}{12} ).

Since the sum of interior angles of a parallelogram is ( 2\pi ), we can find the other angles.

Let ( \theta ) be the measure of one of the other angles. We have:

( \theta + \frac{11\pi}{12} = \pi )

Solving for ( \theta ), we get:

( \theta = \pi - \frac{11\pi}{12} = \frac{12\pi}{12} - \frac{11\pi}{12} = \frac{\pi}{12} )

So, each of the other two angles is ( \frac{\pi}{12} ).

Now, we can use trigonometry to find the lengths of the other two sides. Since we have a right triangle formed by one of the sides (4), the height (12), and the angle ( \frac{\pi}{12} ), we can use the tangent function:

( \tan(\frac{\pi}{12}) = \frac{\text{opposite}}{\text{adjacent}} )

( \tan(\frac{\pi}{12}) = \frac{h}{4} )

Solving for ( h ), we get:

( h = 4 \tan(\frac{\pi}{12}) )

Using a calculator, we find:

( h \approx 4 \times 0.2679 \approx 1.0716 )

So, the lengths of the other two sides are approximately 1.0716. Therefore, the other two sides are approximately 1.0716 units long.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7