Question

express tan r as a fraction in simplest terms.
answer attempt 1 out of 5
tan r =

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle R\), the side opposite to \(\angle R\) is \(ST = 27\), and the side adjacent to \(\angle R\) is \(RS=36\).

Step2: Calculate \(\tan R\)

\(\tan R=\frac{ST}{RS}\)
Substitute \(ST = 27\) and \(RS = 36\) into the formula: \(\tan R=\frac{27}{36}\)
Simplify the fraction \(\frac{27}{36}\) by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 27 and 36 is 9.
\(\frac{27\div9}{36\div9}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)