# Thread: Triangle measurements

1. ## Triangle measurements

Triangle

xz=18.5 m
xy=12.2 m
∠x= 73°

use the given measurements to find each of the following:
A. YZ
B. M
∠XZY
C. M∠xyz
D. The area

2. This is a classic case for the law of cosines and the law of sines.

Let XZ = a, XY = b, YZ = c. Then, by the law of cosines:

$c^2 = a^2 + b^2 - 2ab \cos 73$.

After you calculate c, then use the law of sines to find the angles:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin 73}$

3. How do you find yz?

4. I defined the length of YZ as c. Since you know the lengths of XZ (a) and XY (b), and the measure of the angle they share (ZXY = C = 73 degrees), you can use the law of cosines to find the length of YZ (c).
The calculation is $c^2 = (18.5)^2 + (12.2)^2 - 2(18.5)(12.2)\cos 73$.