Question

What is the measure of angle Q to the nearest whole degree?
43°
49°
53°
58°

Answer 1

Answer:

m∠Q ≈ 53°

Step-by-step explanation:

To find the measure of ∠Q, the law of cosines will need to be used. Lowercase letters represent the side lengths, while upper case letters represent angles.

In this situation, 'A' will be ∠Q. Therefore:

17² = 18² + 20² -2(18)(20)cosQ

Simplify:

289 = 324 + 400 -2(360)cosQ

Continue simplifying down:

-435 = -720cosQ

Divide both sides by '-720':

0.604 = cosQ

$cos^{-1}Q = 0.604$

m∠Q ≈ 52.83 or 53° rounded to the nearest whole degree.

Answer 2

Based on the calculations, the measure of angle Q to the nearest whole degree is equal to 53°.

How to calculate the measure of angle Q?

Based on the triangle attached in the image above, we can deduce the following parameters:

• Side QM = 18 units.

• Side MN = 17 units.

• Side QN = 20 units.

In this scenario, we would apply the cosine trigonometry function to determine the measure of angle Q:

MN² = QM² + QN² - 2(QM)(QN)cosθ

17² = 18² + 20² - 2(18)(20)cosθ

289 = 324 + 400 - 720cosθ

720cosθ = 724 - 289

720cosθ = 435

θ = cos⁻¹(435/720)

θ = cos⁻¹0.6042

θ = 52.8 ≈ 53°.

Read more on cosine function here: brainly.com/question/4599903

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