Question

find the length of the missing leg in the provided triangle. note that the diagram may not be to scale. 10 3 81 9

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the legs. Let the unknown leg be \(x\). Given one leg \(a = 12\) and the hypotenuse \(c = 15\). Then \(x^{2}+12^{2}=15^{2}\), which can be rewritten as \(x^{2}=15^{2}-12^{2}\).

Step2: Calculate squares

Calculate \(15^{2}=225\) and \(12^{2}=144\). So \(x^{2}=225 - 144\).

Step3: Subtract

\(x^{2}=81\).

Step4: Find the square - root

Take the square - root of both sides. Since \(x\) represents the length of a side of a triangle, we consider the positive square - root. So \(x=\sqrt{81}=9\).

Answer:

9