Question

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

Answer 1

Answer:

19/20

Step-by-step 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, $\displaystyle{ \cos(\angle M)=\sin (\angle L)= \frac{19}{20}$.


(Take a look at the picture. From the definition of trigonometric ratios in right triangles we have :
$\displaystyle { \sin(\angle L)= \frac{opposite \ side}{hypotenuse} = \frac{19}{20}.$
and
 $\displaystyle { \cos(\angle M)= \frac{adjacent \ side}{hypotenuse} = \frac{19}{20}.$)

Answer: 19/20