Question

solve for a.
a = ?

Explanation:

Step1: Identify geometric theorem

This uses the geometric mean (altitude) theorem for right triangles: the altitude to the hypotenuse is the geometric mean of the two segments it creates on the hypotenuse.

Step2: Set up the formula

$$a = \sqrt{2 \times 8}$$

Step3: Calculate the product

$$2 \times 8 = 16$$

Step4: Compute the square root

$$\sqrt{16} = 4$$

Answer:

4