The angle of elevation is \( \square \) degrees. (Round to the nearest degree.) 107 feet tall casts a shadow 110 feet long. Find the angle of elevation of the sun to the nearest degree.

To find the angle of elevation of the sun, we can use the tangent function, which relates the angle of elevation to the opposite side (the height of the object) and the adjacent side (the length of the shadow) in a right triangle. Here, we have: - Height (opposite) = 107 feet - Shadow (adjacent) = 110 feet Using the formula: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{107}{110} \] Calculating this gives: \[ \theta = \tan^{-1}\left(\frac{107}{110}\right) \approx \tan^{-1}(0.9727) \approx 44.9^\circ \] Rounding this to the nearest degree, the angle of elevation is approximately \( 45^\circ \). Using trigonometry can be extremely helpful in various real-life scenarios! For instance, when assessing how high to build a structure or estimating flight paths for drones, understanding angles of elevation can make a huge difference in planning and safety. Additionally, common mistakes when dealing with angles and shadows often include forgetting to round appropriately or misapplying trigonometric functions. Always check your calculations and remember the context of the shadows; they can change with time of day and season, affecting your angle!