**Contents**

### Using Sine

- The trigonometric identity for sine tells us that for a right-angled triangle:

\sin (\theta)=\frac{O}{H}

Where O is the length of the edge opposite the angle θ and H is the length of the hypotenuse.

Example

We wish to find the unknown angle, θ, in the above right-angled triangle. As we have the lengths of the hypotenuse and opposite side, we can use sine to do this:

\sin (\theta) =\frac{O}{H}=\frac{5}{7}

\theta =\sin ^{-1}\left(\frac{5}{7}\right)=45.58^{\circ}