A triangle has sides A,B, and C. If the angle between sides A and B is #(pi)/4#, the angle between sides B and C is #pi/4#, and the length of B is 9, what is the area of the triangle?

1 Answer
Binayaka C.
Apr 3, 2016

The Area of the triangle #=20.25# units

Explanation:

Opposite angle of side C is #/_C=pi/4=180/4=45^0#
Opposite angle of side A is #/_A=pi/4=180/4=45^0 :./_B=180-(45+45)=90^0# Using sine law #A/sinA=B/sinB or A=9*(sin45/sin90)=9/sqrt2#Since it is a right angled isocelles triangle, Side # B=9/sqrt2# The Area of the triangle #= 1/2*C*A # or Area#=1/2*9/sqrt2*9/sqrt2 = 81/4 =20.25 # Units[Ans]

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