Question

find the value of tan y rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Find the length of \( XY \)

Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \). Let \( a = 12 \), \( c = 13 \), and \( b=XY \).

$$
LATEXBLOCK0
$$

Step2: Calculate \( \tan Y \)

The formula for tangent in a right - triangle is \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle Y \), the opposite side to \( \angle Y \) is \( WX = 12 \) and the adjacent side is \( XY = 5 \).

$$ \tan Y=\frac{WX}{XY}=\frac{12}{5}=2.4 $$

Answer:

\( 2.4 \)