Question

find the value of x. round the answer to the nearest tenth if necessary. (not drawn to scale) a 3.2 b 2 c 6.3 d 7.6

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 7\), \(a = 3\), and \(b=x\). So, \(x=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 7\) and \(a = 3\) into the formula: \(x=\sqrt{7^{2}-3^{2}}=\sqrt{49 - 9}=\sqrt{40}\).

Step3: Simplify and round

\(\sqrt{40}\approx6.3\) (rounded to the nearest tenth).

Answer:

C. 6.3