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Find the value of the variable in the picture below. round to the nearest tenth if necessary

Find the value of the variable in the picture below. round to the nearest tenth if-example-1

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To find the angles shown we need to remember the definition of the tangent function:


\tan \theta=\frac{\text{opp}}{\text{adj}}

In the case for angle x we notice that the opposite leg is 1 and the adjacent leg is 3, plugging this values in the equation above and solving for x we have:


\begin{gathered} \tan x=(1)/(3) \\ x=\tan ^(-1)((1)/(3)) \\ x=18.4 \end{gathered}

In the case for angle y we notice that the opposite leg is 3 and the adjacent leg is 1, plugging this values in the equation above and solving for y we have:


\begin{gathered} \tan y=(3)/(1) \\ y=\tan ^(-1)((3)/(1)) \\ y=71.6 \end{gathered}

Therefore, x=18.4° and y=71.6°

User Rishabh Saxena
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