Question

13)Given triangle XYZ as shown at right find YZ rounded to the nearest tenth

Answer 1

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:

$\frac{YZ}{sin(X)} = \frac{XZ}{sin(Y)}$

Using the values, we get:

$\frac{XZ}{sin(96)} = \frac{35}{sin(55)} \\ \\ XZ= \frac{35*sin(96)}{sin(55)} \\ \\ XZ=42.5$

Thus the value of YZ, rounded of to nearest tenth will be 42.5