Question

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

Explanation:

Step1: Find the length of side \( TU \)

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

Step2: Recall the tangent ratio formula

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

Answer:

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