A hill is at 4 km horizontal distance from a trekker’s position as marked on the map. If an aerial radar measures the distance to the top of the shed on the top of the hill as 5 km, what height is the hill relative to the position of the trekker?

🧠 Explanation:

A hill 4 km horizontally from a trekker, with a 5 km aerial distance to its top, has a height of 3 km. Using the Pythagorean theorem for a right triangle (horizontal distance² + height² = aerial distance²), calculate: 4² + h² = 5², so 16 + h² = 25, h² = 9, h = 3 km. Studied in geometry, this applies to navigation and surveying. The calculation ensures accurate elevation estimates, critical for trekking, engineering, or mapping, highlighting the practical use of mathematics in real-world spatial analysis.