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. ยท 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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