GATE 2023 CE (CE2) – Question 46
A delivery agent is at a location R. To deliver the order, she is instructed to travel to location P along straight-line paths of RC, CA, AB and BP of 5 km each. The direction of each path is given in the table below as whole circle bearings. Assume that the latitude (L) and departure (D) of R is (0, 0) km. What is the latitude and departure of P (in km, rounded off to one decimal place)?
| Path | RC | CA | AB | BP |
|---|---|---|---|---|
| Direction (degrees) | 120 | 0 | 90 | 240 |
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (B) L = 0.0; D = 5.0
Explanation
For each path of length 5 km with whole circle bearing $\theta$,
$$\text{Latitude}=5\cos\theta\ (\text{north}),\qquad\text{Departure}=5\sin\theta\ (\text{east}).$$
| Path | $\theta$ | Latitude | Departure |
|---|---|---|---|
| RC | 120° | $5\cos120^\circ=-2.5$ | $5\sin120^\circ=+4.330$ |
| CA | 0° | $+5.0$ | $0$ |
| AB | 90° | $0$ | $+5.0$ |
| BP | 240° | $5\cos240^\circ=-2.5$ | $5\sin240^\circ=-4.330$ |
**Sums:**
- Latitude of P $=-2.5+5+0-2.5=\mathbf{0.0}$ km
- Departure of P $=4.330+0+5-4.330=\mathbf{5.0}$ km
So P is at $(L,D)=(0.0,\ 5.0)$ (option B).