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?

Answer 1

sqrt 13

Explanation:

sqrt 13 = 3.6055

Answer 2

We can use law of cosines to find the length of the third side.

Law of cosines is:

c^2 = a^2 + b^2 - 2ab*cos(C), where angle C is opposite of side c.

Plug in what we know.

c^2 = 3^2 + 4^2 - 2(3)(4)cos(60)

Simplify:

c^2 = 9 + 16 - 24cos(60)

c^2 = 25 - 24cos(60)

Solve for c by taking the square root of both sides:

c = sqrt(25 - 24cos(60))

c = sqrt(25 - 24(0.5))

c = sqrt(13)

c = 3.606