Question

Suppose a triangle has two sides of length 3 and 4 and that the angle between these two sides is 60°. What is the length of the third side of the triangle?

A) 3
B) Square root 13
C) 4 Square root 3
D) Square root 3

Answer 1

B) Square root 13

Explanation:

AP3X

Answer 2

sqrt(13)

B

Explanation:

This problem uses the Cos law

Givens

• a = 3
• b = 4
• C = 60 degrees

Formula

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

Solution

• c^2 = a^2 + b^2 - 2*a*b*Cos(C) Substitute givens
• c^2 = 3^2 + 4^2 - 2*3*4*Cos(60) Evaluate
• cos(60) = 1/2 Evaluate
• c^2 = 9 + 16 - 2* 3 * 4 * 1/2 Add the first two term. The third term is 12
• c^2 = 25 - 12 Subtract
• c^2 = 13 Take the square root of both sides.
• c = sqrt(13) Answer