Question

express tan p as a fraction in simplest terms.

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ for an acute angle $\theta$. For $\angle P$ in right - triangle $PQR$, the side opposite to $\angle P$ is $QR$ and the side adjacent to $\angle P$ is $PQ$.

Step2: Identify the lengths of the sides

We are given that $QR = 15$ and $PQ=29$.

Step3: Calculate $\tan P$

Using the tangent formula $\tan P=\frac{QR}{PQ}$, substituting the values we get $\tan P=\frac{15}{29}$.

Answer:

$\frac{15}{29}$