Question

question
find the length of the third side. if necessary, round to the nearest tenth.
answer attempt 1 out of 2

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Let the two legs be \(a = 10\) and \(b\) (the unknown side), and the hypotenuse \(c=14\). Then \(b^{2}=c^{2}-a^{2}\).

$$b^{2}=14^{2}-10^{2}$$

Step2: Calculate \(14^{2}\) and \(10^{2}\)

\(14^{2}=196\), \(10^{2} = 100\). So \(b^{2}=196 - 100\).

$$b^{2}=96$$

Step3: Find \(b\)

\(b=\sqrt{96}\approx9.8\) (rounded to the nearest tenth)

Answer:

\(9.8\)