In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Diagram
x = ?
y = ?
z = ?
Step 02:
Similar Triangles
[tex]\frac{15}{z}=\frac{z}{20}[/tex]
15 * 20 = z * z
300 = z ²
[tex]z\text{ = }\sqrt[]{300}[/tex]
x ² + 15 ² = z ²
[tex]\begin{gathered} x^2+225=(\sqrt[]{300})^2 \\ x^2=300\text{ - 225} \\ x\text{ = }\sqrt[]{75} \end{gathered}[/tex]
y² + z² = 20²
[tex]\begin{gathered} y^2+(\sqrt[]{300})^2=400 \\ y^2=400-300 \\ y=\sqrt[]{100}\text{ = 10} \end{gathered}[/tex]
The answer is:
x = √75 = 5√3
y = 10
z = √300 = 10√3
