Question

In this right triangle LMN L and M are complentary angles and sin (L) is 19\20 what is cos (M)

Answer 1

19/20

Explanation:

Answer 2

In any right triangle ABC, with right angle A we have the following:


`\sin(\angle B)=\cos(\angle C)`

and


`\sin(\angle C)=\cos(\angle B)`.


This means that the sine of a non 90° angle, is equal to the cosine of its complementary angle.


Thus,
`\displaystyle{ \cos(\angle M)=\sin (\angle L)= (19)/(20)`.


(Take a look at the picture. From the definition of trigonometric ratios in right triangles we have :

`\displaystyle { \sin(\angle L)= (opposite \ side)/(hypotenuse) = (19)/(20).`
and

`\displaystyle { \cos(\angle M)= (adjacent \ side)/(hypotenuse) = (19)/(20).`)

Answer: 19/20