We have the measure of 2 angles of the triangle. Since the sum of all 3 angles of a triangle must be 180 degrees, we can write:
X+ Y + Z = 180
X + 55 + 29 = 180
⇒ X = 96 degrees
We can find the measure of YZ using the law of sines. Writing the law of sines for given triangle:
[tex] \frac{YZ}{sin(X)} = \frac{XZ}{sin(Y)} [/tex]
Using the values, we get:
[tex] \frac{XZ}{sin(96)} = \frac{35}{sin(55)} \\ \\
XZ= \frac{35*sin(96)}{sin(55)} \\ \\
XZ=42.5[/tex]
Thus the value of YZ, rounded of to nearest tenth will be 42.5
