Answer:
The answer to your question is z = [tex]\sqrt{24}[/tex]
Step-by-step explanation:
Process
I'll solve this problem using proportions, I hope it helps you
We consider the adjacent side of both triangle
Adjacent side small triangle = x Adjacent side big triangle = 10
Proportion of these sides = [tex]\frac{x}{10}[/tex]
Now, consider the opposite side of both triangles
Opposite side fo small triangle = 2 Opposite side big triangle = x
Proportion = [tex]\frac{2}{x}[/tex]
Now, equal both proportions and solve for x
[tex]\frac{x}{10} = \frac{2}{x}[/tex]
x² = 20
x = [tex]\sqrt{20}[/tex]
x = 2[tex]\sqrt{5}[/tex]
Using Geometric mean
x = [tex]\sqrt{2x10} = \sqrt{20}[/tex]
Using the Pythagorean theorem to find z
z² = (√20)² + 2²
z² = 20 + 4
z² = 24
z = [tex]\sqrt{24}[/tex]
