Question

express tan r as a fraction in simplest terms.

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle R$ in right - triangle $RST$, the side opposite to $\angle R$ is $ST$ and the side adjacent to $\angle R$ is $RS$.

Step2: Identify opposite and adjacent sides

We have $ST = 27$ (opposite to $\angle R$) and $RS=36$ (adjacent to $\angle R$).

Step3: Calculate $\tan R$

$\tan R=\frac{ST}{RS}=\frac{27}{36}$.

Step4: Simplify the fraction

We can simplify $\frac{27}{36}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 9. So, $\frac{27\div9}{36\div9}=\frac{3}{4}$.

Answer:

$\frac{3}{4}$