A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #2#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?

1 Answer
Apr 7, 2016

Answer:

≈ 5.36 units

Explanation:

Given a triangle where we are given 2 sides and the angle between them. To find the 3rd side use the #color(blue)" cosine rule " #

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

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

here a = 7 , b = 2 and C# = pi/6 #

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

# c^2 = 7^2 + 2^2 - (2xx7xx2xxcos(pi/6) #

# = 49 + 4 - (28xxcos(pi/6)) = 53 - (24.249)= 28.751 #

now # c^2 = 28.751 rArr c = sqrt28.751 ≈ 5.36 " units "#