Question

find tan (r) given the triangle. enter your answer as a fraction draw

Explanation:

Step1: Recall tangent definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$.

Step2: Identify sides for angle $r$

Opposite side to $r$: $80$, Adjacent side to $r$: $84$.

Step3: Substitute into tangent formula

$\tan(r) = \frac{80}{84}$

Step4: Simplify the fraction

Divide numerator and denominator by 4: $\frac{80\div4}{84\div4} = \frac{20}{21}$

Answer:

$\frac{20}{21}$