Home > Geometry > Perimeter and Area of Triangle

Two corners of a triangle have angles of #pi / 3 # and # pi / 6 #. If one side of the triangle has a length of #1 #, what is the longest possible perimeter of the triangle?

Answer 1

Noah Atkinson

Largest possible perimeter of the triangle is 4.7321

Sum of the angles of a triangle #=pi#

Two angles are #(pi)/6, pi/3# Hence #3^(rd) #angle is #pi - ((pi)/6 + pi/3) = pi/2#

We know# a/sin a = b/sin b = c/sin c#

To get the longest perimeter, length 2 must be opposite to angle #pi/6#

#:. 1 / sin(pi/6) = b/ sin((pi)/3) = c / sin (pi/2)#

#b = (1*sin(pi/3))/sin (pi/6) = 1.7321#

#c =( 1* sin(pi/2)) /sin (pi/6) = 2#

Hence perimeter #= a + b + c = 1 + 1.7321 + 2 = 4.7321#

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

Answer 2

Noah Atkinson

The longest possible perimeter of the triangle can be found by adding the lengths of all three sides together. Use the law of sines to find the lengths of the other two sides of the triangle, then add all three side lengths to get the perimeter.

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

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.