Question

what are the values of cos y and cot x in the triangle below?
cos y = \frac{3}{\sqrt{34}}, cot x = \frac{5}{3}
cos y = \frac{5}{\sqrt{34}}, cot x = \frac{5}{3}
cos y = \frac{5}{\sqrt{34}}, cot x = \frac{3}{5}
cos y = \frac{3}{\sqrt{34}}, cot x = \frac{3}{5}

Explanation:

Step1: Recall cosine formula

$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle Y$, the adjacent - side to $\angle Y$ is $3$ and the hypotenuse is $\sqrt{34}$. So, $\cos Y=\frac{3}{\sqrt{34}}$.

Step2: Recall cotangent formula

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

Answer:

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