Question

find the length of the third side. if necessary, round to the nearest tenth.
24
26
answer
attempt 1 out of 6

Explanation:

Step1: Identify triangle type

This is a right - triangle, so we can use the Pythagorean theorem. Let the two legs be \(a = 24\) and \(b\) (the unknown side), and the hypotenuse be \(c=26\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), and we can also rewrite it as \(b^{2}=c^{2}-a^{2}\) when we want to find a leg.

Step2: Substitute values

Substitute \(a = 24\) and \(c = 26\) into the formula \(b^{2}=c^{2}-a^{2}\). So \(b^{2}=26^{2}-24^{2}\). Calculate \(26^{2}=676\) and \(24^{2}=576\). Then \(b^{2}=676 - 576=100\).

Step3: Solve for b

Take the square root of both sides: \(b=\sqrt{100}=10\).

Answer:

10