Question

an envelope is 7 inches wide, and it measures 8 inches along the diagonal. how tall is the envelope? if necessary, round to the nearest tenth.
inches

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle (the envelope is a rectangle, and the diagonal forms a right - triangle with length and width), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (diagonal), and \(a\) and \(b\) are the legs (width and height of the envelope). Let the width \(a = 7\) inches, the diagonal \(c = 8\) inches, and the height be \(b\). We can rewrite the formula to solve for \(b\): \(b=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute the values

Substitute \(a = 7\) and \(c = 8\) into the formula: \(b=\sqrt{8^{2}-7^{2}}=\sqrt{64 - 49}=\sqrt{15}\)

Step3: Calculate the approximate value

\(\sqrt{15}\approx3.9\) (rounded to the nearest tenth)

Answer:

\(3.9\)