Question

find the value of tan m rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Recall tangent definition

In right triangle, $\tan M = \frac{\text{opposite}}{\text{adjacent}}$ to $\angle M$.

Step2: Identify sides

Opposite side: $ON = \sqrt{41}$; Adjacent side: $MN = 30$.

Step3: Calculate value

$\tan M = \frac{\sqrt{41}}{30} \approx \frac{6.403}{30} \approx 0.2134$

Step4: Round to hundredth

$0.2134 \approx 0.21$

Answer:

0.21