Question

Find the length in feet of a leg of a right triangle whose Hypotenuse is 12 feet and the other leg is 96 inches. Round to the nearest 10th as needed

Answer 1

Given:-

The length in feet of a leg of a right triangle whose Hypotenuse is 12 feet and the other leg is 96 inches.

To find:-

The length of other leg.

Now we convert 96 inches into feet,

$96\text{inches}=8\text{feet}$

Let the unknow side length be x.

Now we use the pythogoras theorem. so we get,

$\begin{gathered} x^2+8^2=12^2 \\ x^2+64=144 \\ x^2=144-64 \\ x^2=80 \\ x=\sqrt[]{80} \end{gathered}$

By furthur simplification. we get,

$\begin{gathered} \sqrt[]{80}=\sqrt[]{16\times5} \\ \text{ =4}\sqrt[]{5} \end{gathered}$

So the length of other side is,

$\begin{gathered} 4\sqrt[]{5}=4\times2.236 \\ \text{ =}8.944 \\ \text{ =8.9} \end{gathered}$

So the value is 8.9 feet.