Question

practice - radical equations and applications
18 points possible answered: 15/18
question 13
find the length of the hypotenuse of the triangle pictured below. give your answer accurate to at least 2
decimal places.
hypotenuse = submit question

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 7\) and \(b = 8\), and hypotenuse \(c\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 7\) and \(b = 8\) into the formula: \(c=\sqrt{7^{2}+8^{2}}\).

Step2: Calculate \(a^{2}+b^{2}\)

First, calculate \(7^{2}=49\) and \(8^{2}=64\). Then \(a^{2}+b^{2}=49 + 64=113\). So \(c=\sqrt{113}\).

Step3: Find the square - root value

Using a calculator, \(\sqrt{113}\approx10.63014581\). Rounding to two decimal places, we get \(c\approx10.63\).

Answer:

\(10.63\)