A fence 2.4 m tall, is 10 m away from a tree of height 16 m . Calculate the angle of elevation of the top of the tree from the top of the fence.

To solve this, we can use the tangent function from trigonometry. The height difference between the tree and the fence is \(16 m - 2.4 m = 13.6 m\). Since the distance from the fence to the tree is 10 m, we can use the tangent of the angle of elevation (let's call it θ) as follows: \[ \tan(θ) = \frac{\text{height difference}}{\text{distance}} = \frac{13.6 m}{10 m} \] Now, calculating the angle: \[ θ = \tan^{-1}(1.36) \approx 54.5^\circ \] So, the angle of elevation from the top of the fence to the top of the tree is approximately 54.5 degrees. Isn't it fascinating how simple trigonometric functions can help us understand the world around us, like determining angles from various objects? This technique can also be useful in construction or landscaping, where precise measurements can help create beautiful and functional spaces. For those who love a deeper dive into the topic, you can explore more about the applications of trigonometry in real life, especially in areas like architecture, engineering, and even astronomy! Books and resources on geometry often contain practical applications that make the subject come alive in exciting ways.