Question

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

Answer 1

`\sin\theta=(12)/(13)`

Explanation:

The sine function relates the side opposite the angle with the hypotenuse, in this case, we know it is the adjacent side and the hypotenuse.

We calculate the value of the opposite side by means of the Pythagorean theorem, just like this:

`\begin{gathered} c^2=a^2+b^2 \\ \\ 13^2=5^2+b^2 \\ \\ b^2=169-25 \\ \\ b=√(144) \\ \\ b=12 \end{gathered}`

Therefore, the value of the sine of the angle would be:

`\begin{gathered} \sin\theta=\frac{\text{ opposite}}{\text{ hypotenuse }} \\ \\ \sin\theta=(12)/(13) \end{gathered}`