Question

multiple choice 1 point
write the tangent ratios for \\( \angle p \\) and \\( \angle q \\).
not drawn to scale
\\( \tan p=\frac{20}{12}, \tan q=\frac{12}{20} \\)
\\( \tan p=\frac{12}{16}, \tan q=\frac{16}{12} \\)
\\( \tan p=\frac{16}{12}, \tan q=\frac{12}{16} \\)
\\( \tan p=\frac{20}{16}, \tan q=\frac{16}{20} \\)

Explanation:

Step1: Recall the tangent ratio formula

The tangent of an angle in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Find \(\tan P\)

For \(\angle P\), the side opposite to \(\angle P\) is \(RQ = 16\) and the side adjacent to \(\angle P\) is \(FR=12\). So, \(\tan P=\frac{16}{12}\).

Step3: Find \(\tan Q\)

For \(\angle Q\), the side opposite to \(\angle Q\) is \(FR = 12\) and the side adjacent to \(\angle Q\) is \(RQ = 16\). So, \(\tan Q=\frac{12}{16}\).

Answer:

\(\tan P=\frac{16}{12},\tan Q=\frac{12}{16}\) (corresponds to the third option)