The angle of elevation from a point 50 meters away from the base of a tower to the top of the tower is 30 degrees. Find the height of the tower.

Sun, 10 May 2026 15:59:00 +0000

**The angle of elevation from a point 50 meters away from the base of a tower to the top of the tower is 30 degrees. Find the height of the tower.** Curious minds often seek simple yet precise calculations in architecture, engineering, and everyday problem solving—like determining the height of a tower standing tall above a familiar distance. When someone stands 50 meters from the base of a tower and measures an angle of elevation of exactly 30 degrees to the top, it’s not just a math quiz—it’s a gateway to understanding how perspective and geometry shape perception. With modern interest growing in accessible STEM applications, especially in surveying, construction planning, and digital visualization tools, understanding this angle translates into practical insights for professionals and informed citizens alike. ### Why the angle of elevation from a point 50 meters away from the base of a tower to the top of the tower is 30 degrees? Find the height of the tower. This scenario is grounded in fundamental trigonometry. The angle of elevation is the upward angle from a horizontal viewpoint to a vertical object, and when paired with the known distance from the base and the angle, it creates a right triangle. With the distance of 50 meters (the adjacent side) and the angle of 30 degrees, trigonometric ratios—specifically the tangent function—enable an accurate height calculation. Because tan(30°) ≈ 0.577, dividing the base distance by this value reveals the symbolic height: roughly 50 ÷ 0.577 ≈ 86.6 meters. This straightforward method underpins precise measurements used in urban planning, signal tower construction, and virtual modeling—where even small errors compound across large scales.