A guy wire is stretched from the top of a \( 200-\mathrm{ft} \) transmission tower to a point on the ground 130 ft from the center of the base of the tower. What angle, in degrees, does the guy wire make with the ground?

To find the angle that the guy wire makes with the ground, we can use trigonometry, specifically the tangent function. The height of the tower (opposite side) is \(200\) ft, and the distance from the base of the tower to the point on the ground (adjacent side) is \(130\) ft. We use the tangent function: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{200}{130} \] Now, let's calculate \(\theta\): \[ \theta = \tan^{-1}\left(\frac{200}{130}\right) \approx \tan^{-1}(1.5385) \approx 56.3^\circ \] So, the angle that the guy wire makes with the ground is approximately \(56.3\) degrees. Now you can enjoy a cozy chat about angles and towers! Isn't it interesting how these mathematical concepts come to life in real-world structures like transmission towers? It's like giving a new voice to those tall metallic giants! If you're ever puzzled by trigonometry, remember: it's all about relationships between angles and sides. Try drawing a right triangle and labeling the sides for a visual aid. You'll find that mistakes often happen when the labels get mixed up—keep it clear, and you'll do great!