Hot Air Balloon Adventure: Trigonometry in Action
What is the relation between the height of the balloon at point P and the distance between points A and B?
(a) z = 30
(b) d = 31
(c) ≤ 37
(d) 3 ≥
When the balloon rises further by 50 meters, what is the relation between the new height and d?
Final answer: The relation between the height of the balloon at point P and the distance between point A and B can be expressed as z = d * tan(30°). The relation between the new height and d after the balloon rises further by 50 meters at point A can be expressed as d = (z + 50) / tan(45°)
Answer:
The relation between the height of the balloon at point P and the distance between points A and B is z = d * tan(30°). When the balloon rises further by 50 meters, the relation between the new height and d is d = (z + 50) / tan(45°).
Embark on a thrilling journey with Lakshman as he rides high above in a hot air balloon, exploring the wonders of trigonometry in action! The hot air balloon, powered by the magic of heated air lifting it gracefully into the sky, presents a perfect scenario to apply mathematical principles to solve real-world problems.
As Lakshman reaches a height at point P and spots a lorry parked at B with an angle of depression of 30°, the relation between the balloon's height and the distance between points A and B can be expressed as z = d * tan(30°). This equation helps us understand how the balloon's altitude is influenced by the distance between its location and the objects below.
Furthermore, when the balloon rises further by 50 meters at point A and Lakshman spots the same lorry at an angle of depression of 45°, we can determine the new height of the balloon and its relation to the distance parameter d. The equation d = (z + 50) / tan(45°) enables us to calculate the updated height based on trigonometric principles.
Trigonometry not only adds a layer of complexity to mathematical problem-solving but also showcases its practical applications in scenarios like tracking the movement of a hot air balloon in the sky. Explore more mathematical concepts and their real-world implications to broaden your knowledge and sharpen your problem-solving skills!