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

1 Answer
Jim G.
Apr 7, 2016

≈ 11.745 units

Explanation:

In this situation where we have a triangle with 2 sides and the angle between them known , and we wish to find the 3rd side , then we use the #color(blue)" cosine rule " #

# c^2 = a^2 + b^2 - (2abcosC) #

where a and b are the 2 given sides and C , the angle between them. c , is the side to be found.

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

substitute these values into the #color(blue)" cosine rule "#

# c^2 = 12^2 + 5^2 - (2xx12xx5xxcos((5pi)/12))#

# = 144 + 25 -( 120cos((5pi)/12))= 169 -(31.058) #

now # c^2 = 137.942 rArr c = sqrt137.942 ≈ 11.745 " units " #

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