Question

If n = 44 mm and p = 67 mm, what is the measure of angle θ?
A. 41°
B. 57°
C. 49°
D. 33°

Answer 1

Answer: Option C

49°

Step-by-step explanation:

By definition, the cosine of an angle is defined as:

$cos(\theta) = \frac{adjacent}{hypotenuse}$.

The hypotenuse is always the opposite side to the 90 ° angle

The adjacent side is the one that contains the angle theta and the angles of 90 °.

In this case note that:

$adjacent = n = 44\ mm\\\\hypotenuse = p = 67\ mm$

So:

$cos(\theta) = \frac{44}{67}$

$\theta = arcos(\frac{44}{67})$

$\theta =49\°$

Answer 2

Hello!

The answer is:

The correct option is:

C. 49°

Why?

To calculate the measure of the angle, we can use the following trigonometric relation:

$Cos\theta =\frac{Adjacent}{Hypothenuse}$

We are given the following information:

$adjacent=n=44mm\\hypothenuse=p=44mm$

So, substituting and calculating we have:

$Cos(Cos\theta)^{-1} =Cos(\frac{Adjacent}{Hypothenuse})^{-1}\\\\\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}\\\\\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}$

$\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}=Cos(\frac{44}{67})^{-1}=48.95\°=49\°$

Hence, the correct option:

C. 49°

Have a nice day!