Question

a right triangle has a leg of length 16 yards and a hypotenuse of length 23 yards. find the length of the other leg. provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown leg be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. So \(x^{2}+16^{2}=23^{2}\).

Step2: Solve for \(x^{2}\)

\(x^{2}=23^{2}-16^{2}\).
Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(23 + 16)(23-16)=(39)(7)=273\).

Step3: Find \(x\)

\(x=\sqrt{273}\approx16.5\)

Answer:

\(16.5\)