Question

express tan u as a fraction in simplest terms.
answer attempt 1 out of 2
tan u =

Explanation:

Step1: Find the length of \( TU \)

Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \). Let \( a = 12\), \(c = 13\), and \(b=TU\). Then \(TU=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\).

Step2: Calculate \( \tan U \)

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

Answer:

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