Question

find the tangent of ∠y.
w y
65
33
x
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
tan (y) =

Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ to $\theta$.

Step2: Identify sides for $\angle Y$

For $\angle Y$, opposite side is $WX$, adjacent side is $YX$. First, find $WX$ using Pythagoras: $WX = \sqrt{WY^2 - YX^2} = \sqrt{65^2 - 33^2} = \sqrt{(65 - 33)(65 + 33)} = \sqrt{32\times98} = \sqrt{3136} = 56$.

Step3: Calculate $\tan(Y)$

$\tan(Y) = \frac{\text{opposite to } Y}{\text{adjacent to } Y} = \frac{WX}{YX} = \frac{56}{33}$.

Answer:

$\frac{56}{33}$