Question

1. - / 1 points find the unknown side of the triangle (in ft). round to the nearest tenth. diagram of right triangle with hypotenuse 23 ft, base 16 ft ft resources read it watch it submit answer

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 \(b\), \(a^{2}+b^{2}=c^{2}\). Let the unknown side be \(a\), the given leg \(b = 16\) ft and the hypotenuse \(c=23\) ft. We want to find \(a\), so we can re - arrange the formula to \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the values

Substitute \(c = 23\) and \(b = 16\) into the formula:
\(a=\sqrt{23^{2}-16^{2}}=\sqrt{(23 + 16)(23 - 16)}\) (using the difference of squares formula \(x^{2}-y^{2}=(x + y)(x - y)\))
First, calculate \(23^{2}=529\) and \(16^{2}=256\). Then \(23^{2}-16^{2}=529 - 256=273\). So \(a=\sqrt{273}\).

Step3: Calculate the square root and round

\(\sqrt{273}\approx16.5\) (rounded to the nearest tenth)

Answer:

\(16.5\)