Question

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

Explanation:

Step1: Identify right triangle sides

In right triangle $\triangle MLN$, $\angle M = 90^\circ$. For $\angle L$, adjacent side $ML = 30$, hypotenuse $LN = 34$. First find opposite side $MN$.
Use Pythagorean theorem: $MN = \sqrt{LN^2 - ML^2}$
$MN = \sqrt{34^2 - 30^2} = \sqrt{1156 - 900} = \sqrt{256} = 16$

Step2: Calculate $\tan L$

$\tan L = \frac{\text{opposite}}{\text{adjacent}} = \frac{MN}{ML}$
$\tan L = \frac{16}{30} \approx 0.53$

Answer:

$0.53$