Answer:
[tex]\text{cos}(M)=\frac{19}{20}[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given that in right triangle LMN, L and M are complementary angles and [tex]\text{sin}(L)=\frac{19}{20}[/tex]. We are asked to find the [tex]\text{cos}(M)[/tex].
We know that sine relates opposite side of right triangle to hypotenuse.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
We also know that cosine relates adjacent side of right triangle to hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see from the attachment that LM is hypotenuse and MN is adjacent side of our given triangle.
[tex]\text{cos}(M)=\frac{19}{20}[/tex]
Therefore, [tex]\text{cos}(M)[/tex] is [tex]\frac{19}{20}[/tex] as well.
