Question

what are the values of sin x and tan y in the triangle below? sin x = 3/√34, tan y = 3/5; sin x = 5/√34, tan y = 5/3; sin x = 5/√34, tan y = 3/5; sin x = 3/√34, tan y = 5/3

Explanation:

Step1: Recall sine formula

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\sin X$, the opposite - side to angle $X$ is $3$ and the hypotenuse is $\sqrt{34}$. So, $\sin X=\frac{3}{\sqrt{34}}$.

Step2: Recall tangent formula

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\tan Y$, the opposite - side to angle $Y$ is $5$ and the adjacent - side is $3$. So, $\tan Y = \frac{5}{3}$.

Answer:

$\sin X=\frac{3}{\sqrt{34}},\tan Y=\frac{5}{3}$ (corresponding to the last option in the multiple - choice list)