Question

Can anybody help with this answer?? Use the geometric mean or Pythagorean theorem to solve for z

Answer 1

Answer:

The answer to your question is z = $\sqrt{24}$

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 = $\frac{x}{10}$

Now, consider the opposite side of both triangles

Opposite side fo small triangle = 2  Opposite side big triangle = x

Proportion = $\frac{2}{x}$

Now, equal both proportions and solve for x

                           $\frac{x}{10} = \frac{2}{x}$

                                           x² = 20

                                           x  = $\sqrt{20}$

                                          x = 2$\sqrt{5}$        

Using Geometric mean

x = $\sqrt{2x10} = \sqrt{20}$

Using the Pythagorean theorem to find z    

z² = (√20)² + 2²

z² = 20 + 4

z² = 24

z = $\sqrt{24}$