Question

find the cotangent of ∠x.
triangle with vertices x, y, w (right angle at w), yw = 5, xw = √57, xy = √82
write your answer in simplified, rationalized form. do not round.
cot(x) = blank box fraction and square root buttons

Explanation:

Step1: Recall the definition of cotangent

In a right triangle, the cotangent of an angle is the ratio of the adjacent side to the opposite side. For $\angle X$, we need to identify the adjacent and opposite sides.

Step2: Identify the sides relative to $\angle X$

In right triangle $XWY$ (right - angled at $W$), for $\angle X$:

• The opposite side to $\angle X$ is $WY = 5$.
• The adjacent side to $\angle X$ is $XW=\sqrt{57}$.

Step3: Calculate $\cot(X)$

Using the definition $\cot(\theta)=\frac{\text{adjacent}}{\text{opposite}}$, for $\theta = X$, we have $\cot(X)=\frac{XW}{WY}$.
Substituting the values of $XW=\sqrt{57}$ and $WY = 5$, we get $\cot(X)=\frac{\sqrt{57}}{5}$.

Answer:

$\frac{\sqrt{57}}{5}$