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

Answer:

The correct option is A.

Step-by-step 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.

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

$\cos Z=\frac{\left(21\right)^2+\left(27\right)^2-\left(15\right)^2}{2\left(21\right)\left(27\right)}$

$\cos Z=0.833$

$Z=\cos^{-1}(0.833)$

$Z=33.56^{\circ}$

$Z\approx 34^{\circ}$

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