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

Answer:

$\boxed{b.\:\:\:\sqrt{13}}$

Step-by-step 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;

$\Rightarrow h^2=9+16-24(\frac{1}{2})$

$\Rightarrow h^2=25-12$

$\Rightarrow h^2=13$

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

$\Rightarrow h=\sqrt{13}$

The correct answer is B.