Question

given a right triangle with a hypotenuse length of 20 feet and a leg measuring 12 feet, what is the length of the other leg, in feet? a 8 b 12 c 12√3 d 16 e 32

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Let \(a = 12\), \(c=20\), and we need to find \(b\). Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute the values

Substitute \(a = 12\) and \(c = 20\) into the formula: \(b^{2}=20^{2}-12^{2}\). Calculate \(20^{2}=400\) and \(12^{2}=144\). So \(b^{2}=400 - 144=256\).

Step3: Solve for \(b\)

Take the square root of both sides. Since \(b>0\) (length of a side), \(b=\sqrt{256}=16\).

Answer:

D. 16