Question

use the pythagorean theorem to find the missing length in the right triangle
the missing length is □ (round to one decimal place as needed.)

Explanation:

Step1: Apply Pythagorean Theorem

$$a^{2}+12^{2}=16^{2}$$

Step2: Simplify the equation

$$a^{2}=16^{2}-12^{2}$$
$$a^{2}=256 - 144$$
$$a^{2}=112$$

Step3: Solve for \(a\)

$$a=\sqrt{112}$$
$$a = 4\sqrt{7}\approx10.6$$

Answer:

\(10.6\) cm