Question

Suppose a triangle has 2 sides of length 3 and 4 and that the angle between these two sides is 60 degrees. what is the length of the third side of the triangle?

a. 3
b. sr13
c sr3
d 4sr3

Answer 1

`\boxed{b.\:\:\:√(13)}`

Explanation:

Let the third side of the triangle be
`h\: units`.

We can apply the cosine rule to find
`h`.

`h^2=3^2+4^2-2(3)(4)\cos(60\degree)`

We evaluate to obtain;

`\Rightarrow h^2=9+16-24((1)/(2))`

`\Rightarrow h^2=25-12`

`\Rightarrow h^2=13`

We take the positive square root of both sides to obtain;

`\Rightarrow h=√(13)`

The correct answer is B.