Question

A 12 ft lamppost makes a shadow x ft long when the angle of elevation is 30 degrees. Find x. Round your answer to the nearest hundredth.

Answer 1

We can find the length of x using the tangent trig ratio given to be:

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

From the diagram provided, we have that:

$\begin{gathered} \theta=30\degree \\ opp=12\text{ ft} \\ adj=x \end{gathered}$

Therefore, we can substitute these values into the ratio and solve for x. This is shown below:

$\begin{gathered} \tan 30=\frac{12}{x} \\ \therefore \\ x=\frac{12}{\tan 30} \\ x=20.78\text{ ft} \end{gathered}$

Therefore, the value of x is 20.78 ft.