Question

Given right triangle MNL what is the value of cos(M)?

Answer 1

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 $0.8$