Calculating Building Height using Trigonometry
How can a surveyor determine the height of a building from a distance using trigonometry?
Given that a surveyor stands 1.2 km away from the building and measures an angle of elevation of 24.74°, what steps are involved in calculating the height of the building?
Calculating Building Height using Trigonometry
To determine the height of a building using trigonometry, the surveyor first needs to measure the angle of elevation. In this case, the surveyor stands 1.2 km away from the building and uses a theodolite to measure an angle of elevation of 24.74°. This angle represents the angular separation between the horizontal plane and the line of sight directed towards the highest point of the building.
By applying trigonometric principles, specifically the tangent function, the surveyor can calculate the building's height. The formula involves taking the tangent of the angle of elevation and multiplying it by the distance from the surveyor to the building. This calculation provides an approximation of the building's height above the ground at the surveyor's position.
This method is essential in surveying and geometry for determining inaccessible heights of buildings or structures. It allows surveyors to accurately measure heights from a distance, providing valuable information for various purposes such as construction, architecture, and urban planning.
Understanding Trigonometry in Surveying
Trigonometry plays a crucial role in surveying as it enables surveyors to calculate distances, heights, and angles in inaccessible or remote locations. By utilizing trigonometric functions such as sine, cosine, and tangent, surveyors can determine unknown values based on known measurements.
In the case of calculating building height using trigonometry, the angle of elevation is a key component. It indicates the upward tilt of the theodolite or surveying instrument from the horizontal plane to the point of interest on the building. By measuring this angle accurately, surveyors can make precise calculations for determining building heights.
The tangent function is particularly useful in this scenario, as it relates the angle of elevation to the vertical height of the building. By multiplying the tangent of the angle by the distance from the surveyor to the building, surveyors can obtain an estimate of the building's height above the ground level.
Overall, trigonometry provides surveyors with a powerful tool for spatial analysis and measurement. It enhances the accuracy and efficiency of surveying processes, allowing professionals to collect valuable data and information for various engineering and construction projects.