Question

14 multiple choice 1 point
write the tangent ratios for (angle p) and (angle q).

not drawn to scale
(\bigcirc) (\tan p=\frac{24}{10},\tan q=\frac{10}{24})
(\bigcirc) (\tan p=\frac{26}{24},\tan q=\frac{24}{26})
(\bigcirc) (\tan p=\frac{10}{24},\tan q=\frac{24}{10})
(\bigcirc) (\tan p=\frac{26}{10},\tan q=\frac{10}{26})

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Find \(\tan P\)

For \(\angle P\), the side opposite to \(\angle P\) is \(RQ = 10\) and the side adjacent to \(\angle P\) is \(PR=24\). So, \(\tan P=\frac{10}{24}\).

Step3: Find \(\tan Q\)

For \(\angle Q\), the side opposite to \(\angle Q\) is \(PR = 24\) and the side adjacent to \(\angle Q\) is \(RQ = 10\). So, \(\tan Q=\frac{24}{10}\).

Answer:

\(\tan P=\frac{10}{24},\tan Q=\frac{24}{10}\) (corresponds to the third option)