APSC AE WRD 2019 PYQ: Bearing

Bearing of AC in Equilateral Triangle Multiple Choice Question

Question: ABC is an equilateral triangle. If the bearing of AB is 150°, then the bearing of AC is:
(A) 120°
(B) 210°
(C) 270°
(D) 330°

Answer: (B) 210°

Explanation

In an equilateral triangle ABC, all sides are equal, and all internal angles are 60°. The bearing of line AB is given as 150°, and we need to determine the bearing of line AC. Bearings are measured clockwise from the north (0°).

Calculation Steps

In an equilateral triangle, the angle between any two sides at a vertex (e.g., between AB and AC at point A) is 60°. Since the bearing of AB is 150°, the bearing of AC can be found by considering a clockwise rotation of 60° from AB to AC:

• Bearing of AB = 150°
• Clockwise rotation of 60°: 150° + 60° = 210°
• Thus, the bearing of AC = 210°

Alternatively, a counterclockwise rotation of 60° from AB would yield 150° - 60° = 90°, but since bearings are measured clockwise from north, the clockwise rotation is appropriate.

Key Notes

• In an equilateral triangle, the internal angle between any two sides is always 60°, which affects the relative bearings of the sides.
• Bearings are measured clockwise from north, a standard convention in surveying and navigation.
• This concept is critical in surveying and civil engineering for accurately mapping and aligning structures or paths.
• The bearing of AC as 210° is consistent with the geometry of the equilateral triangle and the given bearing of AB.

Note: The bearing of AC in an equilateral triangle with AB at 150° is calculated as 210° by applying a 60° clockwise rotation, ensuring accurate orientation in surveying and civil engineering applications.

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