Question

1. - / 6.76 points find the unknown side of the triangle (in ft). round to the nearest tenth. triangle diagram: right triangle, base 15 ft, hypotenuse 27 ft blank ft

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 hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 27\) ft and one leg \(b = 15\) ft, and we want to find the other leg \(a\). Rearranging the formula for \(a\), we get \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the values

Substitute \(c = 27\) and \(b = 15\) into the formula: \(a=\sqrt{27^{2}-15^{2}}\). First, calculate \(27^{2}=729\) and \(15^{2}=225\). Then, \(27^{2}-15^{2}=729 - 225=504\). So, \(a=\sqrt{504}\).

Step3: Calculate the square root and round

\(\sqrt{504}\approx22.4\) (rounded to the nearest tenth).

Answer:

\(22.4\)