Question

In △PQR, find the measure of ∡P. (A)30.4° (B)59.6° (C)35.9° (D)54.1°

Answer 1

ANSWER

(D)54.1°

EXPLANATION

The measure of angle P can be calculated using the cosine ratio.

We know the adjacent side to angle P to be 33.8 and the hypotenuse of the right triangle is 57.6 units.

$\cos(P) = \frac{adjacent}{hypotenuse}$

$\cos(P) = \frac{33.8}{57.6}$

Take cosine inverse,

$P= \cos ^{ - 1} (\frac{33.8}{57.6} )$

$P=54.07 \degree$

To the nearest tenth, the measure of <P is 54.1°

Answer 2

Hello!

The answer is:

D) 54.1°

Why?

Since we are working with a right triangle, we can use the following equationo to calculate the meause of ∡ P:

$Cos(\alpha )=\frac{adjacent}{hypothenuse}$

$\alpha =cos(\frac{adjacent}{hypothenuse})^{-1}$

We are given that:

$adjacent=33.8\\hypothenuse=57.6$

Now, substituting and calculating, we have:

$P=cos(\frac{33.8units}{57.6units})^{-1}=54.07\°=54.1\°$

Hence the answer is:

D) 54.1°

Have a nice day!