Question

a set of stairs is being built as shown. what is the height of the stair? the stair is □ inches high.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c = 15\) (hypotenuse) and \(b = 9\) (one leg). Let the unknown leg (height of the stair) be \(a\). Then \(a^{2}+9^{2}=15^{2}\).

Step2: Simplify the equation

\(a^{2}+81 = 225\). Subtract 81 from both sides: \(a^{2}=225 - 81\).

Step3: Calculate \(a^{2}\)

\(a^{2}=144\).

Step4: Solve for \(a\)

Take the square root of both sides. Since \(a>0\) (height), \(a=\sqrt{144}=12\).

Answer:

12