A triangle has two corners with angles of # ( pi ) / 2 # and # ( 5 pi )/ 12 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?

1 Answer
Aug 16, 2016

#=6.125#

Explanation:

Clearly this is a right-angled triangle since one of the two given angles is#=pi/2#
Therefore the third angle #=pi-(pi/2+(5pi)/12)=pi-(11pi)/12=pi/12#

In this right angled triangle side#=7# is hypotenuse

Therefore the other sides are

#height=7sin(pi/12)# and

#base=7cos(pi/12)#
Therefore

Area of the triangle

#=1/2times height times base#

#=1/2times7sin(pi/12)times 7cos(pi/12)#

#=1/2times7(0.2588)times 7(0.966)#

#=6.125#