Question

what is the length of the missing leg? if necessary, round to the nearest tenth. a = centimeters

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Here, \(b = 24\), \(c = 40\), and we need to find \(a\). So the equation becomes \(a^{2}+24^{2}=40^{2}\).

Step2: Simplify the equation

First, calculate \(24^{2}=576\) and \(40^{2} = 1600\). Then the equation is \(a^{2}+576=1600\). Subtract 576 from both sides: \(a^{2}=1600 - 576\). So \(a^{2}=1024\).

Step3: Solve for \(a\)

Take the square root of both sides. Since \(a>0\) (length), \(a=\sqrt{1024}\). And \(\sqrt{1024}=32\).

Answer:

\(32\)