A triangle has sides A, B, and C. Sides A and B are of lengths #5# and #6#, respectively, and the angle between A and B is #(5pi)/12 #. What is the length of side C?

1 Answer
Jim G.
Jan 5, 2016

c = 6.74 ( 2 decimal places )

Explanation:

I recommend that you draw a sketch of the triangle where you will see that we are given 2 sides and the included angle ie. the angle between the 2 given sides.

For this condition to find the third side use the cosine rule

# color(red)( c^2 = a^2 + b^2 - ( 2ab cos c ) #

here # a = 5 , b =6 and c =( 5pi) / 12 #

substitute these values into the cosine rule

# rArr c^2 = 5^2 + 6^2 - ( 2 xx 5 xx 6 xx cos((5pi)/12 ) #

evaluating : # c^2 = 25 + 36 - 15.529 #

#rArr c^2 = 45.471 #

At this stage remember to take the square root to get c.

# rArr c = 6.74 # ( 2 decimal places )

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