A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 8, respectively. The angle between A and C is #(11pi)/24# and the angle between B and C is # (5pi)/24#. What is the area of the triangle?

1 Answer
Jim G. · Stefan V.
Jan 3, 2016

#"Area" = 4sqrt(3)# sq. units exactly or 6.9 sq. units (1 decimal place )

Explanation:

I recommend that you draw a sketch of the triangle indicating the lengths of sides and angles given in the question.

Require the angle between A and B which is the third angle in the triangle and since the sum of all 3 angles = #pi#

then

#"3rd angle" = pi - 11pi/24 - 5pi/24#

# = 24pi/24 - 16pi/24#

# = 8pi/24#

# = pi/3#

using

#"Area" = 1/2 xx A xx B xx sin (pi/(3))#

#"Area" = 1/2 xx 2 xx 8 xx sqrt(3 )/2#

#= 8 xx sqrt(3)/2#

#= 4 sqrt(3) " units"^2 ~~ "6.9 units"^2# ( 1 decimal place )

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