Question

the diagram below shows right triangle lmp. which ratio represents the tangent of ∠plm?

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, for an angle \(\theta\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Identify the opposite and adjacent sides for \(\angle PLM\)

For \(\angle PLM\), the side opposite to \(\angle PLM\) is \(MP = 4\) and the side adjacent to \(\angle PLM\) is \(LM=3\).
So, \(\tan\angle PLM=\frac{MP}{LM}\)

Answer:

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