Question

identifying trig ratios (diagram), level 1
question
express \\( \tan u \\) as a fraction in simplest terms.
answer
attempt 3 out of 3
\\( \tan u = \\)

Explanation:

Step1: Find the length of the missing side

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

Step2: Recall the tangent ratio formula

The tangent of an angle 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 \(TU=5\)

Answer:

\(\tan U=\frac{12}{5}\)