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

51

Explanation:

Answer 2

The correct option is third one 51°.

Therefore,

`m\angle Z=51\°`

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=(x^(2)+y^(2)-z^(2))/(2xy)`

Substituting the values we get

`\cos Z=(19^(2)+18^(2)-16^(2))/(2* 19* 18)`

`\cos Z=(429)/(684)=0.6271`

`m\angle Z=\cos^(-1)(0.6271)=51\°`

Therefore,

`m\angle Z=51\°`