A triangle has sides A, B, and C. Sides A and B are of lengths #2# and #1#, respectively, and the angle between A and B is #(5pi)/12 #. What is the length of side C?

1 Answer
Apr 9, 2018

Answer:

#color(blue)("As length of side c cannot be negative", color(brown)(c ~~ 2 " units"#

Explanation:

http://www.gcestudybuddy.com/using-hyperlinks/trigonometry

#"Given : " a = 2, b = 1, hatC = (5pi)/12, " To find c"#

As per the Law of Cosines,

#c^2 = a^2 + b^2 - (2 * a * b * cos C)#

#c = +- sqrt(2^2 + 1^2 - (2 * 2* 1 * cos ((5pi)/12))#

#c = +- sqrt(5 - 4 cos ((5pi)/12)) ~~ 2 " units"#

As length of side c cannot be negative, #color(brown)(c ~~ 2 " units"#