Question

a right triangle with one leg labeled 12, the other leg labeled 8, and the hypotenuse labeled 14.4 (the triangle is drawn on lined paper).

Explanation:

Step1: Identify the triangle type

This is a right - triangle with legs \(a = 12\) and \(b = 8\), and hypotenuse \(c\) (or we can use the Pythagorean theorem to verify the given hypotenuse length). The Pythagorean theorem states that for a right - triangle, \(c=\sqrt{a^{2}+b^{2}}\)

Step2: Calculate the hypotenuse using Pythagorean theorem

Substitute \(a = 12\) and \(b = 8\) into the formula \(c=\sqrt{a^{2}+b^{2}}\)
First, calculate \(a^{2}=12^{2} = 144\) and \(b^{2}=8^{2}=64\)
Then \(a^{2}+b^{2}=144 + 64=208\)
\(c=\sqrt{208}\approx14.4\) (since \(\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}\approx4\times3.6055 = 14.422\approx14.4\))

Answer:

The length of the hypotenuse is approximately \(14.4\) (which matches the given value, and we verified it using the Pythagorean theorem for a right - triangle with legs 12 and 8)