Find the angle of elevation of the sun if a building 125 feet tall casts a shadow 196 feet long. Round to the nearest degree. \( 64^{\circ} \) \( 33^{\circ} \) \( 40^{\circ} \) \( 50^{\circ} \)

To find the angle of elevation of the sun, we can use some trigonometry! The tangent of the angle (θ) is the ratio of the opposite side (the height of the building) to the adjacent side (the length of the shadow). In this case: \[ \tan(θ) = \frac{\text{height of the building}}{\text{length of the shadow}} = \frac{125}{196} \] Now calculating the angle, we take the arctangent: \[ θ = \tan^{-1}\left(\frac{125}{196}\right) \] Using a calculator, we find that \(θ\) is approximately \(33^\circ\). So, the angle of elevation of the sun is \(33^{\circ}\)! It’s interesting to note that the angle of elevation can vary dramatically depending on the time of year and location. In summer, the sun is higher in the sky, leading to a more vertical shadow, while in winter, shadows lengthen as the sun sits lower on the horizon. So, next time you’re outside on a sunny day, remember – you’re not just soaking up the rays, but also getting a lesson in geometry! If you’re planning outdoor photography or events, knowing the angle of elevation is key! This knowledge can help you determine the best times for lighting—like golden hour when the sun is lower and softens the shadows. Knowing the sun’s position can help you capture better images or create the perfect ambiance for your outdoor space!