Question

given right triangle mno, which represents the value of cos(m)?
$\frac{on}{mn}$
$\frac{mn}{mo}$
$\frac{on}{mo}$
$\frac{mn}{on}$

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$. For $\angle M$:

• Adjacent side to $\angle M$: $MN$ (since $N$ is right angle, $MN$ is adjacent to $\angle M$).
• Hypotenuse: $MO$ (the side opposite the right angle $N$).

Step2: Match with options

Check each option:

• $\frac{ON}{MN}$: $ON$ is opposite $\angle M$, not adjacent. Incorrect.
• $\frac{MN}{MO}$: Adjacent ($MN$) over hypotenuse ($MO$). Correct.
• $\frac{ON}{MO}$: $ON$ is opposite, not adjacent. Incorrect.
• $\frac{MN}{ON}$: $ON$ is opposite, ratio wrong. Incorrect.

Answer:

$\frac{MN}{MO}$ (the second option: $\boldsymbol{\frac{MN}{MO}}$)