Question

question
find the length of the third side. if necessary, round to the nearest tenth.
(image of a right triangle with legs 7 and 8, right angle between them)

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 7\) and \(b = 8\), and we need to find the hypotenuse \(c\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 7\) and \(b = 8\) into the formula \(c=\sqrt{a^{2}+b^{2}}\). So \(a^{2}=7^{2}=49\) and \(b^{2}=8^{2}=64\). Then \(a^{2}+b^{2}=49 + 64=113\). So \(c=\sqrt{113}\).

Step3: Calculate the square root and round

\(\sqrt{113}\approx10.6\) (rounded to the nearest tenth).

Answer:

\(10.6\)