Question

given right triangle mno, which represents the value of cos(m)?
options:

• $\frac{on}{mn}$
• $\frac{mn}{mo}$
• $\frac{on}{mo}$
• $\frac{mn}{on}$

(image: right triangle mno with right angle at n, angle at m is 50°, angle at o is 40°)

Explanation:

Step1: Recall cosine definition

For an acute angle in a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle M$

• Adjacent side to $\angle M$: $MN$
• Hypotenuse of $\triangle MNO$: $MO$

Step3: Substitute into cosine formula

$\cos(M) = \frac{MN}{MO}$

Answer:

$\boldsymbol{\frac{MN}{MO}}$ (Option B)