Question

express tan u as a fraction in simplest terms.

Explanation:

Step1: Find the length of \( TU \)

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

$$
LATEXBLOCK0
$$

Step2: Calculate \( \tan U \)

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

$$ \tan U=\frac{ST}{TU} $$

Answer:

\(\frac{12}{5}\)