Question

find the measure of the two missing sides for each figure below leave answer and rationalized and simplified form

Answer 1

Let's begin by identifying key information given to us:

We have one known angle & one side

`\begin{gathered} \theta=60^(\circ) \\ adjacent(a)=2\sqrt[]{6} \\ opposite(b)=\text{?} \\ hypotenuse(c)=\text{?} \end{gathered}`

Based on the information we have been provided, we will solve for the missing sides using Trigonometric Ratio (SOHCAHTOA). This is shown below:

`\begin{gathered} TOA\Rightarrow\tan \theta=(opposite)/(adjacent) \\ tan\theta=(opposite)/(adjacent) \\ tan60^(\circ)=\frac{opposite}{2\sqrt[]{6}} \\ But,tan60^(\circ)=\sqrt[]{3} \\ opposite=2\sqrt[]{6}\text{ x }\sqrt[]{3} \\ opposite=2\sqrt[]{18} \\ \\ CAH\Rightarrow cos\theta=(adjacent)/(hypotenuse) \\ cos\theta=(adjacent)/(hypotenuse) \\ cos60^(\circ)=\frac{2\sqrt[]{6}}{hypotenuse} \\ But,\cos 60^(\circ)=(1)/(2) \\ hypotenuse\text{ x }\cos 60^(\circ)=2\sqrt[]{6} \\ hypotenuse=\frac{2\sqrt[]{6}}{(1)/(2)} \\ hypotenuse=\frac{2\cdot2\sqrt[]{6}}{1}=4\sqrt[]{6} \\ hypotenuse=4\sqrt[]{6} \end{gathered}`