Question

10 the diagram below shows right triangle lmp. which ratio represents the tangent of ∠plm? 1) 3/4 2) 3/5 3) 4/3 4) 5/4

Explanation:

Step1: Recall the tangent ratio formula

For a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

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

In right - triangle \(LMP\) with respect to \(\angle PLM\), the side opposite to \(\angle PLM\) is \(MP = 4\) and the side adjacent to \(\angle PLM\) is \(LM=3\).

Step3: Calculate the tangent of \(\angle PLM\)

Using the formula \(\tan\angle PLM=\frac{MP}{LM}\), substituting \(MP = 4\) and \(LM = 3\), we get \(\tan\angle PLM=\frac{4}{3}\)

Answer:

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