For angle $A$, which side is the hypotenuse, which side is touching angle $A$ as a leg (adjacent), and which side is across from angle $A$ (opposite)?

In a right triangle, $\cos(\text{angle})$ equals a specific ratio of two sides. Is it opposite/hypotenuse, adjacent/hypotenuse, or opposite/adjacent?

Once you know which side is adjacent to angle $A$ and which is the hypotenuse, form the fraction and reduce it to lowest terms to match an answer choice.

In the expression bar, type 9/15 (this is adjacent over hypotenuse for angle A) and press Enter. Desmos will display this fraction in simplest form; that simplified value is $\cos A$. Compare that simplified fraction to the answer choices.

Angle $C$ is the right angle, so the side opposite it, $AB$, is the hypotenuse. That makes $AC$ and $BC$ the legs of the right triangle.

Look at angle $A$. The two sides that touch angle $A$ are $AB$ and $AC$. Since $AB$ is already the hypotenuse, the leg that is adjacent to angle $A$ is $AC$.

So, relative to angle $A$:

• Adjacent side: $AC = 9$
• Hypotenuse: $AB = 15$

In a right triangle, the cosine of an acute angle is defined as

So for angle $A$,

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

Thus, $\cos A = \frac{3}{5}$, which corresponds to choice D.