Question

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

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°