Given:
It is given that KLM is a right triangle.
The measure of ∠M is 90°
The length of LK is 89, ML is 80 and KM is 39.
We need to determine the ratio that represents the tangent of ∠K.
Measure of tan ∠K:
The measure of tan ∠K can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
From the figure attached below, the side opposite to ∠K is ML and the side adjacent to ∠K is KM
Hence, substituting the values, we get;
[tex]tan \ k=\frac{ML}{KM}[/tex]
where ML = 80 and KM = 39.
Substituting, we get;
[tex]tan \ k=\frac{80}{39}[/tex]
Thus, the ratio that represents the tangent of ∠K is [tex]\frac{80}{39}[/tex]
