di.com/student/practice/678a8aa25b97dcb88cd3be41/class/66cf07a4da0259e398c043ad/uta/678f94d0e86d82059e550b6d/itemid/678a. g. Ratios) BOOKMARK 4 Q + \( \square \) BLAKE SINRAM 16 Kurt spots a bird sitting at the top of a 40ft tall telephone pole. If the angle of elevation from the ground where he is standing to the bird is \( 59^{\circ} \), how many feet is Kurt from the base of the pole?

To determine how far Kurt is from the base of the telephone pole, we can use trigonometry, specifically the tangent function. **Given:** - Height of the telephone pole (opposite side): 40 feet - Angle of elevation: \(59^\circ\) **Objective:** Find the horizontal distance from Kurt to the base of the pole (adjacent side), denoted as \(x\). **Using the Tangent Function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \] Plugging in the known values: \[ \tan(59^\circ) = \frac{40}{x} \] Solving for \(x\): \[ x = \frac{40}{\tan(59^\circ)} \] **Calculating the Value:** 1. Find \(\tan(59^\circ)\): \[ \tan(59^\circ) \approx 1.6643 \] 2. Divide 40 by the tangent of 59 degrees: \[ x = \frac{40}{1.6643} \approx 24.06 \text{ feet} \] **Conclusion:** Kurt is approximately **24.1 feet** away from the base of the telephone pole. **Answer:** Kurt is approximately 24.1 feet from the base of the telephone pole.