Practice Test 7

A student tries to prove $\sin^2\theta + \cos^2\theta = 1$ from a right triangle and writes: “$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$, so $\sin^2\theta + \cos^2\theta = \frac{\text{opposite} + \text{adjacent}}{\text{hypotenuse}} = 1$.” Which statement justifies the identity correctly?

In the right triangle shown, the right angle is at $B$ and the acute angle at $A$ is $\theta$. The hypotenuse $AC$ is labeled $1$. The leg $AB$ is labeled $\cos\theta$ and the leg $BC$ is labeled $\sin\theta$. Which argument uses the Pythagorean Theorem correctly?