Question

find the value of x. round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 20\), \(a=17\), and \(b = x\). So, \(x^{2}+17^{2}=20^{2}\).

Step2: Simplify the equation

\(x^{2}=20^{2}-17^{2}\).
Since \(20^{2}=400\) and \(17^{2}=289\), then \(x^{2}=400 - 289=111\).

Step3: Solve for \(x\)

\(x=\sqrt{111}\approx10.5\) (rounded to the nearest tenth).

Answer:

\(10.5\)