A triangle has sides A, B, and C. Sides A and B are of lengths #2# and #3#, respectively, and the angle between A and B is #(5pi)/12 #. What is the length of side C?

1 Answer
Jim G.
Feb 5, 2016

C ≈ 3.15

Explanation:

In this question since 2 sides A and B of the triangle are known as is the angle between them then use

# color(blue)(" Cosine Rule ") color(black)(" stated below ") #

for this triangle :

# C^2 = A^2 + B^2 - ( 2AB costheta) #

where #theta color(black)(" is angle between A and B") #

here A = 2 , B = 3 and #theta =( 5pi)/12#

#rArr C^2 = 2^2 + 3^2 - ( 2 xx 2 xx 3 xx cos((5pi)/12) #

# rArr C^2 = 4+9 - (12 xx cos((5pi)/12) ≈9.9#

( remember this is #C^2 )#

# rArr C = sqrt9.9 ≈ 3.15#

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