Proving the Pythagorean Identity Practice Test

Start with $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, then add to get $\frac{\text{opposite}+\text{adjacent}}{\text{hypotenuse}}=1$.

Start with $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, then square and use $\text{opposite}^2+\text{adjacent}^2=\text{hypotenuse}^2$.

Because $\theta$ is acute, $\sin^2\theta+\cos^2\theta=2\sin\theta\cos\theta$ and this equals $1$.

Start with $\sin\theta=\frac{\text{hypotenuse}}{\text{opposite}}$ and $\cos\theta=\frac{\text{hypotenuse}}{\text{adjacent}}$, then square and add to get $1$.