A triangle has two corners with angles of # pi / 12 # and # pi / 2 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-01-11T11:12:23

Area of the largest possible triangle is #91.44# sq.unit.

Angle between sides # A and B# is # /_c= pi/12=15^0#

Angle between sides # B and C# is # /_a= pi/2=90^0 :.#

Angle between sides # C and A# is # /_b= 180-(15+90)=75^0#

For largest area of triangle #7# should be smallest side , which

is opposite to the smallest angle #:. C=7#

The sine rule states if #A, B and C# are the lengths of the sides

and opposite angles are #a, b and c# in a triangle, then:

#A/sina = B/sinb=C/sinc ; C=7 :. A/sina=C/sinc# or

#A/sin90=7/sin15 :. A= 7* sin90/sin15~~ 27.05(2dp)#

Now we know sides #A=27.05 , C=7# and their included angle

#/_b = 75^0#. Area of the triangle is #A_t=(A*C*sinb)/2#

#:.A_t=(27.05*7*sin75)/2 ~~ 91.45# sq.unit.

Area of the largest possible triangle is #91.44# sq.unit [Ans]