Question

find the exact length of the missing side of the right triangle.

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Here, \(b = 5\), \(c=7\), and we need to find \(a\).

Step2: Substitute values into the formula

$$a^{2}+5^{2}=7^{2}$$
$$a^{2}+25 = 49$$

Step3: Solve for \(a^{2}\)

$$a^{2}=49 - 25$$
$$a^{2}=24$$

Step4: Find \(a\)

$$a=\sqrt{24}$$
Simplify \(\sqrt{24}=\sqrt{4\times6}=2\sqrt{6}\)

Answer:

\(2\sqrt{6}\)