Two corners of a triangle have angles of # ( pi )/ 2 # and # ( pi ) / 6 #. If one side of the triangle has a length of # 8 #, what is the longest possible perimeter of the triangle?

Answer 1

#24+8sqrt3#

the 3 angles: #pi/2,pi/3,pi/6# in order for the sides to be the greatest, we need 8 to be opposite of the smallest angle. thus, the other sides will be #8sqrt(3) and 16# (30,60,90 triangle) thus the perimeter will be #8+8sqrt(3)+16=24+8sqrt3#
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Answer 2

To find the longest possible perimeter of the triangle given that two corners have angles ( \frac{\pi}{2} ) and ( \frac{\pi}{6} ), proceed as follows:

  1. Identify the third angle of the triangle using the fact that the sum of angles in a triangle is ( \pi ).
  2. Determine the side lengths of the triangle using trigonometric relationships, specifically the sine and cosine functions.
  3. Use the Law of Sines or Law of Cosines to find the lengths of the other sides of the triangle.
  4. Calculate the perimeter of the triangle using the lengths of its sides.
  5. Maximize the perimeter by adjusting the lengths of the sides accordingly.

By following these steps, you can determine the longest possible perimeter 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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