Question

Check my answer please?

3. In triangle XYZ, XY = 15, YZ = 21, and XZ = 27. What is the measure of angle Z to the nearest degree?

A. 34***
B. 39
C. 56
D. 117

Thanks!!

Answer 1

you are right Elrd23 .......................

Answer 2

The correct option is A.

Explanation:

Given information: In triangle XYZ, XY = 15, YZ = 21, and XZ = 27.

It means z=15, x=21, y=27.

Using Law of Cosine.

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

`\cos Z=(\left(21\right)^2+\left(27\right)^2-\left(15\right)^2)/(2\left(21\right)\left(27\right))`

`\cos Z=0.833`

`Z=\cos^(-1)(0.833)`

`Z=33.56^(\circ)`

`Z\approx 34^(\circ)`

The measure of angle Z is approx 34 degree. Therefore option A is correct.