A triangle has two corners with angles of # ( pi ) / 2 # and # ( 5 pi )/ 12 #. If one side of the triangle has a length of #9 #, what is the largest possible area of the triangle?

Question

1063 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-06T09:53:27

The area is #=151.1u^2#

The third angle of the triangle is

#=1/2pi-5/12pi=1/12pi#

To have the largest possible area, the side of length #9# is opposite
the smallest angle, i.e, #1/12pi#

Let the side opposite the angle #5/12pi# be #=a#

Applying the sine rule to the triangle,
#a/sin(5/12pi)=9/sin(1/12pi)#

Therefore,

#a=9*sin(5/12pi)/sin(1/12pi)=33.6#

The area of the triangle is

#A=1/2*9*33.6=151.1#