Question

identifying trig ratios (diagram), level 1
question
express \\( \tan u \\) as a fraction in simplest terms.
answer
attempt 1 out of 3
\\( \tan u = \\)
submit answer
\\( \sqrt { - } \\)
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Explanation:

Step1: Find the length of the missing side

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Let \(a = 12\), \(c = 13\), and solve for \(b\) (the side adjacent to \(U\)).
\(b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\)

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 is \(ST = 12\) and the adjacent side is \(TU=5\)
\(\tan U=\frac{12}{5}\)

Answer:

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