Question

Answer must be in simplest form

Answer 1

The trigonometric ratios shows that the cos M is 4/5.

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: $hypothenuse^2=(leg_1)^2+(leg_2)^2$ . And the main trigonometric ratios are: sin $\alpha$,  cos $\alpha$ and tan $\alpha$, where:

$sin \alpha =\frac{opposite\;leg}{hypotenuse} \\ \\ cos \alpha =\frac{adjacent\;leg}{hypotenuse} \\ \\ tan \alpha =\frac{opposite\;leg}{adjacent\;leg}$

For finding the cos M, firstly, you should find the side MN from Pythagorean Theorem.

$hypothenuse^2=(leg_1)^2+(leg_2)^2\\ \\\ 30^2=18^2+(MN)^2\\ \\ 900=324+(MN)^2\\ \\(MN)}^2=900-324\\ \\ (MN)^2=576\\ \\ MN=24$

If MN=24, the cos M will be

$cosM =\frac{adjacent\;leg}{hypotenuse} =\frac{24}{30} =\frac{4}{5}$

Learn more about  cosine of an angle  here:

brainly.com/question/11967894

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