For angle $P$, which sides form this angle? One of them is the hypotenuse; the other is the adjacent leg to angle $P$.

In a right triangle, $\cos(\text{angle})$ equals $\dfrac{\text{adjacent}}{\text{hypotenuse}}$. Use the side lengths given for angle $P$ to form this ratio and then simplify the fraction.

From the geometry of the triangle, express $\cos P$ as $\dfrac{\text{adjacent leg to }P}{\text{hypotenuse}}$. Using the given side lengths, this becomes a numerical fraction.

Type that fraction (for example, 9/15) into Desmos and note the decimal value it gives.

Convert each answer choice to a decimal in Desmos (e.g., type 3/4, 4/3, etc.) and see which one matches the decimal value you found for $\cos P$. That matching choice is the correct answer.

In right triangle $PQR$, $\angle Q$ is the right angle, so the side opposite this angle, $PR$, is the hypotenuse. We are told $PR = 15$.

Angle $P$ is formed by sides $PQ$ and $PR$.

• $PR$ is the hypotenuse.
• The other side touching angle $P$ is $PQ$, which is the adjacent leg to angle $P$.

We are told $PQ = 9$, so for angle $P$:

• Adjacent side = $PQ = 9$
• Hypotenuse = $PR = 15$.

By definition in a right triangle,

For angle $P$:

Now simplify $\frac{9}{15}$ by dividing numerator and denominator by their greatest common factor, $3$:

So $\cos P = \frac{3}{5}$.