Question

question 2
what is the length of \\( \overline { e f } \\) in the right triangle below?
\\( \bigcirc e f = 5 7 6 \\)
\\( \bigcirc e f = 1 6 \\)
\\( \bigcirc e f = 2 6 0 \\)
\\( \bigcirc e f = 2 4 \\)

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(DEF\) with \(DE = 26\) (hypotenuse), \(DF=10\) (one leg), and \(EF\) (the other leg). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let \(a = DF = 10\), \(c=DE = 26\), and \(b = EF\). Then \(EF^{2}+DF^{2}=DE^{2}\), so \(EF^{2}=DE^{2}-DF^{2}\).

Step2: Substitute values

Substitute \(DE = 26\) and \(DF = 10\) into the formula: \(EF^{2}=26^{2}-10^{2}\). Calculate \(26^{2}=676\) and \(10^{2}=100\). Then \(EF^{2}=676 - 100\).

Step3: Simplify

\(EF^{2}=576\). Take the square root of both sides. Since \(EF>0\) (length), \(EF=\sqrt{576}\).

Step4: Calculate square root

\(\sqrt{576}=24\).

Answer:

\(EF = 24\)