A triangle has two corners with angles of # pi / 2 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #4 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-07-03T11:51:18

The area of the triangle is #=19.3u^2#

The third angle of the triangle is

#=1/2pi-3/8pi=1/8pi#

To have the largest possible area, the side of length #4# is opposite
the smallest angle, i.e, #1/8pi#

Let the side opposite the angle #3/8pi# be #=a#

Applying the sine rule to the triangle,

#a/sin(3/8pi)=4/sin(1/8pi)#

Therefore,

#a=4*sin(3/8pi)/sin(1/8pi)=9.66#

The area of the triangle is

#A=1/2*4*9.66=19.3#