Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 8.8\) and \(a=8.5\), we need to find \(b\). So \(b^{2}=c^{2}-a^{2}\).

$$b^{2}=8.8^{2}-8.5^{2}$$

Step2: Calculate \(8.8^{2}\) and \(8.5^{2}\)

$$8.8^{2}=(8 + 0.8)^{2}=8^{2}+2\times8\times0.8+0.8^{2}=64+12.8 + 0.64=77.44$$

$$8.5^{2}=(8+0.5)^{2}=8^{2}+2\times8\times0.5 + 0.5^{2}=64 + 8+0.25 = 72.25$$

Step3: Subtract

$$b^{2}=77.44-72.25=5.19$$

Step4: Find \(b\)

$$b=\sqrt{5.19}\approx2.3$$

Answer:

\(2.3\)