Answer:
XZ = 6 units
YZ = 10.39 units
Step-by-step explanation:
We were given the following information:
The figure is a right triangle having one known side and three known angles (90 degrees, 30 degrees & 60 degrees)
XZ = 12
XY = ?
YZ = ?
Part A
We are to calculate the length of side XY. This is shown below:
Since we have one known side and three known angles, we can obtain the length of XY using the Trigonometric Ratio (SOHCAHTOA):

XY = 6 units
Part B
We are to calculate the length of side YZ. Since this is a right triangle, we can solve it using 2 different methods as shown below:
Method 1 (Trigonometric Ratio):

Method 2 (Pythagoras Theorem):
![\begin{gathered} \text{Pythagoras Theorem is given by:} \\ c^2=a^2+b^2 \\ where\colon \\ c=hypotenuse=XZ=12 \\ a=side_1=YZ=\text{?} \\ b=side_2=XY=6 \\ \text{Substituting the variables into the formula, we have:} \\ 12^2=a^2+6^2 \\ 144=a^2+36 \\ \text{Subtract ''36'' from both sides, we have:} \\ 144-36=a^2 \\ 108=a^2 \\ a^2=108 \\ \text{Take the square root of both sides, we have:} \\ a=\sqrt[]{108} \\ a=10.392\approx10.39 \\ a=10.39 \\ a=YZ\Rightarrow YZ=10.39 \\ YZ=10.39units \\ \\ \therefore YZ=10.39units \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/sv4447axd62sfqm2jn2yj07ajadbhg9lnt.png)
YZ = 10.39 units