Question

Suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is 60°. What is the length of the third side of the triangle?

A. /3
B. /7
C. 2 /3
D. 2

Answer 1

There is a photo with equations and the answer.

Answer 2

`\text{The length of third side is }\sqrt7 units`

Explanation:

Given that a triangle has two sides of length 2 and 3 and that the angle between these two sides is 60°.

Let b=2 units and c=3 units

we have to find the length of the third side of the triangle.

By law of cosines

`a^2=b^2+c^2-2bc\cosA`

where A is the angle between the side b and c

`a^2=2^2+3^2-2(2)(3)\cos60`

`a^2=4+9-6=7`

`a=\pm\sqrt7`

Length cannot be negative

∴
`a=\sqrt7 units`

Option B is correct.