Angle Of Elevation Formula

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Angle of elevation is the angle formed when the observer is looking at an object located at a height greater than the observer. Angle of elevation is the angle taken of the observer with respect to the horizontal line of axis. Angle of elevation is evaluated using any of the trigonometric functions based on the given situation in a problem.

Example 1: Find the angle of elevation if the observer is looking at the top of a building of height 45m above the ground. The observer is at a distance 60m away from the base of the building.

Given height above the ground, AB = 45m

Distance of the observer from the base, BO = 60m

Let the angle of elevation = θ



Now in triangle ABO, tanθ = AB/BO = 45/60 = 3/4
Hence angle of elevation, θ = tan-1(3/4) = 36.87°


Example 2: A person is looking at the top of a tree located at a distance of 14ft away from him. If the height of the tree is 25ft, then find the angle of elevation to the top of the tree.

Given height of the tree = 25ft

Distance between the person and the base of the tree = 14ft

Let the angle of elevation to the top of the tree = θ

Then, tanθ = Opposite length/Adjacent length = 25/14 = 1.786

Hence angle of elevation, θ = tan-1(1.786) = 60.75°


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