Step \(1\)
Find the length of the side MN
we know that
Applying the Pythagorean Theorem
\(ML^{2} =NL^{2} +MN^{2}\)
Solve for MN
\(MN^{2}=ML^{2} -NL^{2}\)
in this problem
\(ML=25\ units\\ NL=15\ units\)
Substitute in the formula above
\(MN^{2}=25^{2} -15^{2}\)
\(MN^{2}=400\)
\(MN=20\ units\)
Step \(2\)
Find the value of cos (M)
we know that
in the right triangle MNL
\(cos (M)=\frac{adjacent\ side\ angle\ M}{hypotenuse}\)
\(adjacent\ side\ angle\ M=MN=20\ units\\ hypotenuse=ML=25\ units\)
Substitute
\(cos (M)=\frac{20}{25}\)
\(cos (M)=\frac{4}{5}\)
\(cos (M)=0.8\)
therefore
The answer is
The value of cos(M) is equal to \(0.8\)
