Question

find the missing length of t 5.6 in. 10.6 in. a a > in. 5

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. Here \(c = 10.6\) in and \(b = 5.6\) in, and we want to find \(a\). So \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

\(a=\sqrt{(10.6)^{2}-(5.6)^{2}}=\sqrt{(10.6 + 5.6)(10.6 - 5.6)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
\(=\sqrt{(16.2)\times(5)}=\sqrt{81}\).

Step3: Calculate the square - root

\(a = 9\) in.

Answer:

9 in