Question

Solve for the missing side lengths.60°9yA. O x = 18, y = 9/3B.2 = 18, y = 183C. O rx = 18/3, y = 36DOC36, y183

Answer 1

Given the information on the right triangle, we can use the cosine function to find the hypotenuse:

`\begin{gathered} \cos (60)=\frac{\text{adjacent side}}{hypotenuse}=(9)/(x) \\ \Rightarrow\cos (60)=(9)/(x) \end{gathered}`

solving for x, we get:

`\begin{gathered} \cos (60)=(1)/(2) \\ \Rightarrow\cos (60)=(9)/(x) \\ \Rightarrow(1)/(2)=(9)/(x) \\ \Rightarrow(x)/(2)=9 \\ \Rightarrow x=9\cdot2=18 \\ x=18 \end{gathered}`

next, we can use the tangent function to find y:

`\begin{gathered} \tan (60)=\frac{\text{opposite side}}{adjacent\text{ side}}=(y)/(9) \\ \Rightarrow\tan (60)=(y)/(9) \end{gathered}`

doing the same for y, we get:

`\begin{gathered} \tan (60)=\sqrt[]{3} \\ \Rightarrow\tan (60)=(y)/(9) \\ \Rightarrow\sqrt[]{3}=(y)/(9) \\ \Rightarrow y=9\cdot\sqrt[]{3} \end{gathered}`

therefore, x = 18 and y = 9*sqrt(3)