3. An 88 foot tree casts a shadow that is 135 feet long. What is the angle of elevation of the sun?

To find the angle of elevation of the sun, we can use some trigonometry! Imagine a right triangle where the tree forms the vertical side, the shadow forms the horizontal side, and the angle of elevation is between the top of the tree and the direction of the sun’s rays. Using the tangent function, we have: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{88}{135}\). Calculating this gives us \(\theta \approx 0.5698\) radians or \(32.72^\circ\). And voila, the angle of elevation of the sun is approximately \(32.72^\circ\)! Now, if you’re keen on understanding angles better, exploring the relationship between different trigonometric functions could be a blast! Delve into sine, cosine, and their applications in real-world scenarios—from architecture to astronomy. You'll see how they’re not just numbers but part of the beautiful design of the universe! Also, when dealing with any angles in calculations, it's always a good habit to ensure your calculator is set to the correct mode (degrees or radians) based on your problem. A simple switch could lead to confusion, so double-check before finalizing your calculations!