Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a = 2 inches and c = 6 inches, what is b? if necessary, round to the nearest tenth. b = inches

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute given values

Given \(a = 2\) and \(c = 6\), then \(b^{2}=6^{2}-2^{2}=36 - 4=32\).

Step3: Solve for \(b\)

\(b=\sqrt{32}\approx5.7\) (rounded to the nearest tenth).

Answer:

\(5.7\)