Question

The law of cosines is used to find the measure of Angle Z. Triangle X Y Z is shown. The length of X Y is 16, the length of Y Z is 19, and the length of X Z is 18. To the nearest whole degree, what is the measure of Angle Z? 41º 47º 51º 57º

Answer 1

Answer:

The correct option is third one  51°.

Therefore,

$m\angle Z=51\°$

Step-by-step explanation:

Given:

In Triangle XYZ

XY = z = 16

YZ = x = 19

ZX = y = 18  

To Find

angle Z = ?

Solution:

In Triangle XYZ, Cosine Rule says

$\cos Z=\dfrac{x^{2}+y^{2}-z^{2}}{2xy}$

Substituting the values we get

$\cos Z=\dfrac{19^{2}+18^{2}-16^{2}}{2\times 19\times 18}$

$\cos Z=\dfrac{429}{684}=0.6271$

$m\angle Z=\cos^{-1}(0.6271)=51\°$

Therefore,

$m\angle Z=51\°$

Answer 2

Answer:

51

Step-by-step explanation: