The error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
<h3>What is Tangent (Tanθ)?</h3>
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
Tan(θ) = Perpendicular/Base
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Given the uppermost portion of a that is 3.0m long stadia rod is inclined 14 cm toward the observer, therefore, the angle of inclination, θ can be written as
tan(θ)=0.14/3
θ = 2.672°
Also, the rod intercept is 1.75m, therefore, t the error in distance in the distance is,
tanθ=x/1.75
x = 1.75 tan(θ)
x = 1.75 × tan(2.672°)
x = 0.08167 m = 8.167 cm
Hence, the error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
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