For angle $R$, which side is directly across from it (does not touch $R$)? Which non-hypotenuse side touches $R$? Label these as opposite and adjacent.

Remember that $\tan(\text{angle})$ in a right triangle is defined in terms of the opposite and adjacent legs. Which side length should go on top of the fraction and which on the bottom?

Once you know which sides are opposite and adjacent to angle $R$, plug in their given lengths to form the correct ratio and then match it to one of the answer choices.

After deciding which sides are opposite and adjacent to angle $R$, create a new expression in Desmos that divides the opposite side length by the adjacent side length (for example, opposite ÷ adjacent using the given leg lengths). Note the decimal value Desmos gives for this ratio.

In separate lines, type each answer choice exactly as a fraction (for example, 8/15, 15/8, etc.) and let Desmos convert them to decimals. The correct choice is the one whose decimal value matches the decimal from the opposite/adjacent ratio you found in the previous step.

Angle $S$ is the right angle, so the side across from $\angle S$ is the hypotenuse.

• The side across from $\angle S$ is $RT$, so $RT$ is the hypotenuse.
• The remaining two sides, $RS$ and $ST$, are the legs of the triangle.

Focus on angle $R$:

• The opposite side to angle $R$ is the side that does not touch $R$: this is $ST$.
• The adjacent side to angle $R$ (that is not the hypotenuse) is the side that touches $R$: this is $RS$.

So, for angle $R$:

• Opposite side: $ST$
• Adjacent side: $RS$

By definition,

So for angle $R$,

We are given $ST = 15$ and $RS = 8$, so

Thus, the value of $\tan R$ is $\dfrac{15}{8}$, which corresponds to choice B.