Question

which trigonometric ratios are correct for triangle xyz? check all that apply. tan(y) = 8/15 cos(x) = 15/17 tan(x) = 15/8 sin(y) = 8/17 cos(y) = 8/17

Explanation:

Step1: Find hypotenuse XY

Use Pythagorean theorem:
$$XY = \sqrt{YZ^2 + XZ^2} = \sqrt{15^2 + 8^2} = \sqrt{225+64} = \sqrt{289} = 17$$

Step2: Verify tan(Y)

$\tan(Y)=\frac{\text{opposite}}{\text{adjacent}}=\frac{XZ}{YZ}=\frac{8}{15}$ ✔️

Step3: Verify cos(X)

$\cos(X)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{XZ}{XY}=\frac{8}{17}$ ❌

Step4: Verify tan(X)

$\tan(X)=\frac{\text{opposite}}{\text{adjacent}}=\frac{YZ}{XZ}=\frac{15}{8}$ ✔️

Step5: Verify sin(Y)

$\sin(Y)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{XZ}{XY}=\frac{8}{17}$ ✔️

Step6: Verify cos(Y)

$\cos(Y)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{YZ}{XY}=\frac{15}{17}$ ❌

Answer:

• $\tan(Y) = \frac{8}{15}$
• $\tan(X) = \frac{15}{8}$
• $\sin(Y) = \frac{8}{17}$