Question

find the length of the third side of the right triangle. give an exact answer and an approximation to three decimal places if needed. the length of the third side is (simplify your answer. type an integer or a decimal )

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 100\) and \(a = 96\), and we want to find \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(b=\sqrt{100^{2}-96^{2}}=\sqrt{(100 + 96)(100 - 96)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).

Step3: Calculate the values inside the square - root

\((100 + 96)(100 - 96)=(196)\times(4)=784\).

Step4: Find the square - root

\(b=\sqrt{784}=28\)

Answer:

28