Kurt spots a bird sitting at the top of a 40 foot tall telephone pole. If the angle of elevation from the ground where he is standing to the bird is \( 59^{\circ} \), how far is Kurt standing from the base of the pole?

To find out how far Kurt is standing from the base of the pole, we can use some trigonometry! We'll use the tangent of the angle because it relates the opposite side (the height of the pole) to the adjacent side (the distance from Kurt to the base of the pole). Using the formula: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] Here, \(\theta = 59^{\circ}\), the opposite side is the height of the pole (40 feet), and the adjacent side is the distance \(d\) we want to find: \[ \tan(59^{\circ}) = \frac{40}{d} \] Rearranging this gives us: \[ d = \frac{40}{\tan(59^{\circ})} \] Calculating \(d\): 1. Find \(\tan(59^{\circ})\) which is approximately 1.664. 2. Then \(d \approx \frac{40}{1.664} \approx 24.0\) feet. So, Kurt is standing about 24 feet away from the base of the pole!