In ΔLMN, the measure of ∠N=90°, ML = 97, NM = 65, and LN = 72. What ratio represents the tangent of ∠L?

The tangent of ∠L represents the ratio between side NM and side LN.

The value of this tangent is 0.9028

Step-by-step explanation:

The angle ∠N is 90°, so we have a right triangle. In a right triangle, the tangent of an angle represents the ratio between the opposite side of that angle and the adjacent side (the cathetus, not the hypotenusa) of that angle.

So, in the triangle LMN, the opposite side to the angle ∠L is NM, and the adjacent side is LN (ML is the hypotenusa, because it is the bigger side). The value of this tangent is:

tan (L) = NM / LN = 65 / 72 = 0.9028