Question

find the length of the missing leg in the provided triangle. note that the diagram may not be to scale. 8 more questions to go

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Let the missing leg be \(x\), the given legs are \(12\) and \(x\), and the hypotenuse \(c = 15\). So \(x^{2}+12^{2}=15^{2}\).

Step2: Rearrange the formula

We get \(x^{2}=15^{2}-12^{2}\). Calculate \(15^{2}=225\) and \(12^{2}=144\). Then \(x^{2}=225 - 144=81\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (length cannot be negative), \(x=\sqrt{81}=9\).

Answer:

9