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A triangle has two corners with angles of # pi / 12 # and # pi / 3 #. If one side of the triangle has a length of #14 #, what is the largest possible area of the triangle?

Answer 1

Evelyn Arboleda

The area of the triangle is #=669.4u^2#

The third angle of the triangle is

#=pi-(1/12pi+1/3pi)#

#=pi-5/12pi#

#=7/12pi#

The angles are

#1/12pi, 5/12pi, 7/12pi#

To have the greatest area , the side of length #14# is opposite the smallest angle

We apply the sine rule

#14/sin(1/12pi)=A/sin(5/12pi)=B/sin(7/12pi)#

#A=14sin(5/12pi)/sin(1/12pi)=52.2#

#B=14sin(7/12pi)/sin(1/12pi)=99.1#

The area of the triangle is

#=1/2*AB*sin(1/12pi)#

#=0.5*52.2*99.1*sin(1/12pi)#

#=669.4#

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Answer 2

Carson Arnold

The largest possible area of the triangle is 49 square units.

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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.