Question

an envelope is 15 inches wide, and it measures 17 inches along the diagonal. how tall is the envelope? inches

Explanation:

Step1: Apply Pythagorean theorem

Let the width be $a = 15$, the diagonal be $c=17$, and the height be $b$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $a = 15$ and $c = 17$ into the formula $b^{2}=c^{2}-a^{2}$. We get $b^{2}=17^{2}-15^{2}=289 - 225=64$.

Step3: Solve for $b$

Take the square - root of both sides. Since $b>0$, $b=\sqrt{64}=8$.

Answer:

8