Question

9 the diagram below shows right triangle abc. which ratio represents the tangent of ∠abc? 1) 5/13 2) 5/12 3) 12/13 4) 12/5

Explanation:

Step1: Recall the definition of tangent in a right - triangle

In a right - triangle, for an acute angle \(\theta\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).
For \(\angle ABC\), the side opposite to \(\angle ABC\) is \(AC = 5\), and the side adjacent to \(\angle ABC\) is \(BC=12\).

Step2: Calculate \(\tan\angle ABC\)

Using the formula \(\tan\angle ABC=\frac{AC}{BC}\).
Substitute \(AC = 5\) and \(BC = 12\) into the formula, we get \(\tan\angle ABC=\frac{5}{12}\).

Answer:

1. \(\frac{5}{12}\)