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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Find the tangent length if the radius of the curve and its angle were given as 40m and intersection angle 40°.
A) 14.55 m
B) 33.56 m
C) 109.89 m
D) 219.79 m
109.89 m
In simple circular curve surveying, the tangent length is the distance from the point of curve (PC) or point of intersection (PI) to the point of tangency (PT). It is calculated using the formula T=Rtan(D/2), where R is the radius of the curve and D is the deflection angle. When the intersection angle I is provided as 40°, the deflection angle D=180°−I=140°, which yields a tangent length of 109.89 m.
In simple circular curve surveying, the tangent length is the distance from the point of curve (PC) or point of intersection (PI) to the point of tangency (PT). It is calculated using the formula T=Rtan(D/2), where R is the radius of the curve and D is the deflection angle. When the intersection angle I is provided as 40°, the deflection angle D=180°−I=140°, which yields a tangent length of 109.89 m.
D=180°−I — Deflection angle from Intersection angle (I)
T=Rtan(2D) — Tangent length of simple circular curve
The geometry of a simple circular curve connects two straight tangents intersecting at an angle I. The deflection angle D between the tangents equals 180°−I. The tangent length T represents the adjacent side of the right-angled triangle formed by the center of the curve, the point of curve, and the point of intersection, giving T=Rtan(D/2).
The intersection angle I is the interior angle between the back and forward tangents.
The deflection angle D is the angle through which the road or alignment turns (D=180°−I).
Substituting R=40 m and D/2=70° into T=Rtan(D/2) gives T=40×2.74748=109.89 m.
Setting out simple circular curves in highway and railway engineering.
Determining property boundary alignments along curved roadways.
If 40° had been misinterpreted directly as the deflection angle D, the tangent length would be T=40tan(20°)=14.56 m (Option A).
Option B (33.56 m) corresponds to using T=Rsin(70°)=37.58 m minus minor adjustments or common miscalculations.
Option D (219.79 m) represents double the correct tangent length (2T).
C is correct — The deflection angle D=180°−40°=140°, giving a tangent length T=40tan(70°)=109.89 m.
Always read whether the angle given is the 'deflection angle' (D) or the 'intersection angle' (I), as D=180°−I in conventional curve notation.