Question

Consider △LMN.
m∠L + m∠M = °
sin(L) =
sin(M) =

I got y’all

Answer 1

m∠L + m∠M = 90°

sin(L) = cos(M)

sin(M) = cos(L)

lol nice

Answer 2

90°

cos(M)

cos(L)

Explanation:

In a triangle the sum of the three angles is 180°. Here the triangle is a right angled triangle so,

∠L+∠M = 90

which can be seen by adding the angles

42°+48° = 90°

`sin(L)=\frac{\text{Opposite side}}{\text{hypotenuse}}\\\Rightarrow sin (L)=(MN)/(ML)`

`cos(M)=\frac{\text{Adjacent side}}{\text{hypotenuse}}\\\Rightarrow cos(M)=(MN)/(ML)`

∴
`\mathbf{sin(L)=cos(M)=(MN)/(ML)}`

`sin(M)=\frac{\text{Opposite side}}{\text{hypotenuse}}\\\Rightarrow sin (M)=(LN)/(ML)`

`cos(L)=\frac{\text{Adjacent side}}{\text{hypotenuse}}\\\Rightarrow cos(L)=(LN)/(ML)`

∴
`\mathbf{sin(M)=cos(L)=(LN)/(ML)}`