Question

find the length of side a in the right triangle below. use a calculator to estimate the square root to one decimal place. the length of the side, a, is approximately ________. the solution is

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(b = 15\), \(c=17\), and we need to find \(a\). So, \(a^{2}=c^{2}-b^{2}\).
Substitute the values: \(a^{2}=17^{2}-15^{2}\).
Calculate \(17^{2}=289\) and \(15^{2}=225\). Then \(a^{2}=289 - 225\).

Step2: Simplify the equation

\(a^{2}=64\).
Take the square root of both sides: \(a=\sqrt{64}\).
Since \(8\times8 = 64\), \(a = 8\).

Answer:

\(8\)