Question

12 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

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 $24$ and the side adjacent to $\angle P$ is $10$. So, $\tan P=\frac{24}{10}$.

Step3: Find $\tan Q$

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

Answer:

$\tan P=\frac{24}{10},\tan Q=\frac{10}{24}$ (corresponding to the first option in the multiple - choice list)