Question

find the value of tan l rounded to the nearest hundredth, if necessary.
l
n
39
36
15
m
answer attempt 1 out of 3
tan l =
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Explanation:

Step1: Recall tangent ratio

In a right triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\) to angle \(\theta\).
For \(\angle L\) in right triangle \(LMN\) (right - angled at \(M\)):
The side opposite to \(\angle L\) is \(MN = 15\) and the side adjacent to \(\angle L\) is \(LM=36\).

Step2: Calculate \(\tan L\)

Using the tangent ratio formula \(\tan L=\frac{\text{opposite to }L}{\text{adjacent to }L}=\frac{MN}{LM}\)
Substitute \(MN = 15\) and \(LM = 36\) into the formula: \(\tan L=\frac{15}{36}\)
Simplify \(\frac{15}{36}=\frac{5}{12}\approx0.42\) (rounded to the nearest hundredth)

Answer:

\(0.42\)