Question

Find cos 0, where is the angle shown.Give an exact value, not a decimal approximation.

Answer 1

In order to find the cosine of theta, first let's find the length of the third side of the triangle, using Pythagorean theorem:

`\begin{gathered} 13^2=12^2+x^2 \\ 169=144+x^2 \\ x^2=169-144 \\ x^2=25 \\ x=5 \end{gathered}`

The cosine relation is given by the length of the adjacent side to the angle over the length of the hypotenuse.

So we have:

`\cos (\theta)=(5)/(13)`