Question

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

Answer 1

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°