Question

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

Answer 1

the right answer is 19/20 which is A i hope this helps

Answer 2

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)`