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