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