Question

practice writing trigonometric ratios.
consider △lnm.
which statements are true for triangle lnm? check all that apply.
□ the side opposite ∠l is \\(\overline{nm}\\).
□ the side opposite ∠n is \\(\overline{ml}\\).
□ the hypotenuse is \\(\overline{nm}\\).
□ the hypotenuse is \\(\overline{ln}\\).
□ the side adjacent ∠l is \\(\overline{nm}\\).
□ the side adjacent ∠n is \\(\overline{ml}\\).

Explanation:

Step1: Identify right triangle parts

$\triangle LNM$ is right-angled at $M$. Hypotenuse is $\overline{LN}$ (opposite right angle).

Step2: Verify opposite sides

• For $\angle L$: Opposite side is $\overline{NM}$ (non-adjacent to $\angle L$).
• For $\angle N$: Opposite side is $\overline{ML}$ (non-adjacent to $\angle N$).

Step3: Verify adjacent sides

• For $\angle L$: Adjacent side is $\overline{ML}$ (shares vertex with $\angle L$, not hypotenuse), so $\overline{NM}$ is not adjacent.
• For $\angle N$: Adjacent side is $\overline{NM}$ (shares vertex with $\angle N$, not hypotenuse), so $\overline{ML}$ is not adjacent.

Step4: Confirm hypotenuse

Hypotenuse is $\overline{LN}$, not $\overline{NM}$.

Answer:

• The side opposite $\angle L$ is $\overline{NM}$.
• The side opposite $\angle N$ is $\overline{ML}$.
• The hypotenuse is $\overline{LN}$.