Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a = 2.9 centimeters and c = 7.7 centimeters, what is b? if necessary, round to the nearest tenth.
b = centimeters

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 \(a = 2.9\) and \(c = 7.7\), then \(b^{2}=7.7^{2}-2.9^{2}\). First, calculate \(7.7^{2}=7.7\times7.7 = 59.29\) and \(2.9^{2}=2.9\times2.9 = 8.41\). So \(b^{2}=59.29 - 8.41=50.88\).

Step3: Solve for \(b\)

\(b=\sqrt{50.88}\approx7.1\)

Answer:

\(7.1\)