Question

In triangle XYZ, XY = 14, YZ = 22, and XZ = 26. What is the measure of angle Z to the nearest degree?

A. 57°
B. 66°
C. 147°
D. 33°

Answer 1

Answer:

D

WE ARE GOING TO USE THE COSINE RULE

${c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos(c)$

Take the sides as shown in the picture as a,b and c . Substitute the side by using the cosine rule.

${14}^{2} = {22}^{2} + {26}^{2} - 2(22 \times 26) \cos(z)$

$196 = 1160 - 1144 \cos(z)$

$1144 \cos(z) = 1160 - 196$

$\cos(z) = \frac{964}{1144}$

$z = \frac{1}{ \cos} 0.842657342$

1 over cos means cos inverse.

$z = 32.5 nearest \: degree \\ = 33degrees$

ANSWER 33°

Answer 2

Applying the Law of Cosines, the measure of angle Z is: D. 33°.

What is the Law of Cosines?

The Law of Cosines is given as: c² = a² + b² - 2ab(Cos C)

Given:

c = XY = 14

b = YZ = 22

a = XZ = 26

C = angle Z

Plug in the values into the formula for the Law of Cosines:

14² = 26² + 22² - 2(26)(22)(Cos Z)

196 = 1,160 - 1,144(Cos Z)

196 - 1,160 = -1,144(Cos Z)

-964 = -1,144(Cos Z)

-964/-1,144 = Cos Z

Cos Z = 0.8427

Z = cos^-1(0.8427)

Z = 33°

Therefore, applying the Law of Cosines, the measure of angle Z is: D. 33°.

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