Question

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

Explanation:

Step1: Find the length of the missing side

Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 13\) (hypotenuse) and \(a = 12\). Let the missing side be \(b\).

$$b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5$$

Step2: Use the tangent ratio

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 \(TU=5\).
\(\tan U=\frac{ST}{TU}\)

Answer:

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