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?

1 Answer
Jan 11, 2018

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

Explanation:

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]