Answer:
The measure of the angle opposite the leg that is 6 inches long is
\(30^{\circ}\)
Step-by-step explanation:
We have been given sides of right triangle that is we will use pythagoras theorem:
\(hypotenuse^2=side^2+side^2\)
Here, we have one side which is 6 inches
And other side is \(6\sqrt{3}\) inches on substituting the values in the formula above we get:
\(hypotenuse^2=6^2+(6\sqrt{3})^2\)
\(hypotenuse^2=36+108\)
\(\Rightarrow hypotenuse^2=144\)
\(\Rightarrow hypotenuse=12\)
The angle will be \(sin\theta=\frac{perpendicular}{hypotenuse}\)
\(sin\theta=\frac{6}{12}\)
\(\Rightarrow sin\theta=\frac{1}{2}\)
\(\Rightarrow \theta=sin^{-1}(\frac{1}{2})\)
\(\Rightarrow \theta=30^{\circ}\)
Hence, the measure of the angle opposite the leg that is 6 inches long is
\(30^{\circ}\)
