Question

analyzing cofunctions consider △lmn. m∠l + m∠m = sin (l) = sin (m) =

Explanation:

Step1: Recall triangle - angle sum property

In a right - triangle $\triangle LMN$ with $\angle N = 90^{\circ}$, the sum of the non - right angles $\angle L$ and $\angle M$ is $90^{\circ}$ since the sum of all angles in a triangle is $180^{\circ}$ ($m\angle L+m\angle M + m\angle N=180^{\circ}$, and $m\angle N = 90^{\circ}$).

Step2: Use sine function definition

Given $\angle L = 42^{\circ}$, $\sin(L)=\sin(42^{\circ})\approx0.6691$. Given $\angle M = 48^{\circ}$, $\sin(M)=\sin(48^{\circ})\approx0.7431$. But if we consider the options in terms of the angle - related values, we know that for a right - triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse.

Answer:

$m\angle L + m\angle M=90$
$\sin(L)$: (no correct option among given numbers as $\sin(42^{\circ})
eq80,90,180$)
$\sin(M)$: (no correct option among given numbers as $\sin(48^{\circ})
eq80,90,180$)