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Two corners of a triangle have angles of # ( pi )/ 3 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 5 #, what is the longest possible perimeter of the triangle?

Answer 1

Jayden Jackson

Longest possible perimeter of the triangle is

#color(brown)(P = a + b + c ~~ 17.9538#

To find the longest possible perimeter of the triangle.

Given #hatA = pi/3, hatB = pi/4#, one #side = 5#

#hatC = pi - pi/3 - pi/4 = (5pi)/12#

Angle #hatB# will correspond to side 5 to get the longest perimeter.

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Answer 2

Mason Adams

The longest possible perimeter of the triangle is ( 5 + \frac{5\sqrt{3}}{2} + \frac{5\sqrt{2}}{2} ).

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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.