Two corners of a triangle have angles of # (7 pi )/ 12 # and # pi / 8 #. If one side of the triangle has a length of # 6 #, what is the longest possible perimeter of the triangle?

Answer 1

Perimeter # = a + b + c = 6 + 15.1445 + 12.4388 = 33.5833

Three angles are #(7pi)/12, pi/8, (7pi)/24#
To get the longest perimeter, side with length 6 should correspond to least angle of the triangle #(pi/8)#
#6/sin (pi/8) = b / sin ((7pi)/12) = c / sin ((7pi)/ 24)#
#b = (6*sin ((7pi)/12))/sin (pi/8) = 15.1445#
#c =( 6 * sin ((7pi)/24))/sin (pi/8) = 12.4388#

Perimeter # = a + b + c = 6 + 15.1445 + 12.4388 =33.5833

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

To find the longest possible perimeter of the triangle, use the law of sines to determine the lengths of the other two sides, then calculate the perimeter. The formula for the law of sines is:

( \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} )

Given angles: Angle A = ( \frac{7\pi}{12} ) Angle B = ( \frac{\pi}{8} )

Given side length: ( a = 6 )

Find the lengths of the other two sides:

For Angle A: ( \sin(\frac{7\pi}{12}) = \frac{a}{b} ) ( b = \frac{a}{\sin(\frac{7\pi}{12})} )

For Angle B: ( \sin(\frac{\pi}{8}) = \frac{a}{c} ) ( c = \frac{a}{\sin(\frac{\pi}{8})} )

Calculate the lengths: ( b = \frac{6}{\sin(\frac{7\pi}{12})} ) ( c = \frac{6}{\sin(\frac{\pi}{8})} )

Calculate the perimeter: ( \text{Perimeter} = a + b + c )

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