Question

18 multiple choice 1 point
write the tangent ratios for \\( \angle p \\) and \\( \angle q \\).
not drawn to scale
\\( \tan p = \frac { 15 } { 9 }, \tan q = \frac { 9 } { 15 } \\)
\\( \tan p = \frac { 9 } { 12 }, \tan q = \frac { 12 } { 9 } \\)
\\( \tan p = \frac { 12 } { 9 }, \tan q = \frac { 9 } { 12 } \\)
\\( \tan p = \frac { 15 } { 12 }, \tan q = \frac { 12 } { 15 } \\)

Explanation:

Step1: Recall the tangent ratio formula

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

Step2: Find \(\tan P\)

For \(\angle P\), the opposite side to \(\angle P\) is \(RQ = 12\) and the adjacent side is \(PR=9\). So, \(\tan P=\frac{RQ}{PR}=\frac{12}{9}\).

Step3: Find \(\tan Q\)

For \(\angle Q\), the opposite side to \(\angle Q\) is \(PR = 9\) and the adjacent side is \(RQ = 12\). So, \(\tan Q=\frac{PR}{RQ}=\frac{9}{12}\).

Answer:

\(\tan P=\frac{12}{9},\tan Q=\frac{9}{12}\) (corresponds to the third option in the multiple - choice list)