Answer: Bob is looking at a helicopter that is flying 1,000 feet above the ground. Bob is 1,500 feet from the helicopter. At what angle of elevation is Bob looking at the helicopter?

To find the angle of elevation from Bob to the helicopter, you can use the tangent function. The height of the helicopter is 1,000 feet and Bob is 1,500 feet away horizontally. The angle of elevation (θ) can be found using the formula: tan(θ) = opposite/adjacent = 1,000/1,500. Calculating this gives: θ = arctan(1,000/1,500) ≈ 33.69 degrees. So, Bob is looking at the helicopter at an angle of approximately 33.69 degrees above the horizontal! Well, did you know that the concept of angle of elevation can be traced back to ancient civilizations? Scholars like Euclid and Archimedes studied angles and geometric relationships, laying the groundwork for trigonometry. The use of tangents and other functions to calculate angles became crucial for navigators and astronomers centuries later, proving that these angles are not just for math homework but have a rich history intertwined with exploration and discovery! In practice, angles of elevation aren’t just theoretical—they are essential in fields like aviation, architecture, and even drone operation! Knowing how to calculate these angles can help pilots properly approach airstrips during landing or ensure that skyscrapers are designed to meet safety regulations concerning wind load and structural integrity. So whether you're dreaming of flying high or just building the next tallest building, mastering those angles is key!