If right triangle LMN, L and M are complementary angles and sin (L) is 19/20 what is cos (M)

Question

asked Dec 15, 2018 121k views

2 Answers

Rhaldar · Answer 1 · 2018-12-20T12:27:36+0000

Answer: Value of cos(M) is

$\cos M=(19)/(20)$

Explanation:

Since we have given that

LMN is a right angled triangle where L and M are complementary angles ,

And,

$\sin L=(19)/(20)=(Perpendicular)/(Hypotenuse)$

so, we will find base now by using "Pythagorus theorem":

$H^2=B^2+P^2\\\\20^2=B^2+19^2\\\\400=B^2+361\\\\400-361=B^2\\\\39=B^2\\\\√(39)=B$

As we know that side opposite to mentioned theta is considered as perpendicular as shown in the figure ,

For M as
$\theta$

NL will be its perpendicular and MN will be its base and to find the cos(M) we use Base and Hypotenuse.

So, now we will find cos(M) i.e.

$\cos M=(Base)/(Hypotenuse)=(19)/(20)$

Hence,

$\cos M=(19)/(20)$