Answer:
The answer to your question is z = ![\sqrt{24}](https://tex.z-dn.net/?f=%5Csqrt%7B24%7D)
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 = ![\frac{x}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10%7D)
Now, consider the opposite side of both triangles
Opposite side fo small triangle = 2 Opposite side big triangle = x
Proportion = ![\frac{2}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bx%7D)
Now, equal both proportions and solve for x
![\frac{x}{10} = \frac{2}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10%7D%20%3D%20%5Cfrac%7B2%7D%7Bx%7D)
x² = 20
x = ![\sqrt{20}](https://tex.z-dn.net/?f=%5Csqrt%7B20%7D)
x = 2
Using Geometric mean
x = ![\sqrt{2x10} = \sqrt{20}](https://tex.z-dn.net/?f=%5Csqrt%7B2x10%7D%20%3D%20%5Csqrt%7B20%7D)
Using the Pythagorean theorem to find z
z² = (√20)² + 2²
z² = 20 + 4
z² = 24
z = ![\sqrt{24}](https://tex.z-dn.net/?f=%5Csqrt%7B24%7D)