What is the angle of elevation to a building \( 1,000 \mathrm{~m} \) away that is 300 m high? SEE EXAMP

To find the angle of elevation to a building that is 300 m high and 1,000 m away, you can use the tangent function from trigonometry. The angle \( \theta \) is given by: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{300}{1000} \] Calculating this gives: \[ \tan(\theta) = 0.3 \] Now, to find \( \theta \), you take the arctangent: \[ \theta = \tan^{-1}(0.3) \approx 16.7^\circ \] So, the angle of elevation is approximately \( 16.7^\circ \). In real life, understanding angles of elevation can come in handy for various fields such as architecture, where determining the height of structures from a distance is crucial for design and construction planning. For example, engineers can calculate the materials needed and assess safety measures based on these angles. When calculating angles in elevation, a common mistake is forgetting to use the correct opposite and adjacent sides in your tangent ratio. Always double-check your triangle drawing, as mixing up the height and distance can drastically change your angle calculation!