Finding the angle to see the tip of the Maypole using the tangent function.

To find the angle at which you need to look up to see the tip of the Maypole, you can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the Maypole) to the adjacent side (your distance from the Maypole). Here's how you can calculate it: 1. Let's denote the angle you need to find as \(\theta\). 2. The height of the Maypole is 107 feet (opposite side). 3. Your distance from the Maypole is 260 feet (adjacent side). The tangent of the angle \(\theta\) is given by: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{107}{260} \] Using a calculator to find the angle \(\theta\), you can take the arctangent (inverse tangent) of the ratio: \[ \theta = \tan^{-1}\left(\frac{107}{260}\right) \] Doing the calculation: \[ \theta = \tan^{-1}\left(\frac{107}{260}\right) \approx \tan^{-1}(0.4115) \] Using a calculator to find \(\tan^{-1}(0.4115)\): \[ \theta \approx 22.38^\circ \] So, you need to look up at an angle of approximately \(22.38^\circ\) to see the tip of the Maypole.