An aeroplane leaves an airport A and flies on a bearing 035°for 1.5 hours at 600km/hr to airport B It then flies on a bearing 130° for 1.5hours at 400km per hour to an airport C calculate the distance from C to A and the bearing of C from A with the diagram of the bearing
AB = 900km[35o].
BC = 600km[130o].
AC = ?
AC = AB + BC. = 900[35o] + 600[130o]..
AC = (900*sin35+600*sin130) + (900*cos35+600*cos130)I,
AC = 975.8 + 351.6i = 1037km[70.2o].
Bearing of 70.2 Degrees.
Teach me I wan the particular answer of this question plss
D diagram of d question is not here
distance AB = (1.5)(600) km or 900 km
distance BC = 1.5(400) km or 600 km
I assume you drew your diagram correctly.
So now you have triangle ABC with AB = 900, BC = 600 and angle B = 75°
Use the cosine law to find AC
Let me know what you did, and what your answer is.
D diagram wic answers d question is not here
Pleses can u explain more
To solve this problem, we can break it down into two parts:
Part 1: Flight from A to B
1. Start at airport A.
2. Draw a line to represent the bearing of 035°.
3. Multiply the speed of the airplane (600 km/h) by the duration of the flight (1.5 hours) to calculate the distance covered during this leg of the journey.
Part 2: Flight from B to C
4. Start at airport B.
5. Draw a line to represent the bearing of 130° (relative to the line from A to B).
6. Multiply the speed of the airplane (400 km/h) by the duration of the flight (1.5 hours) to calculate the distance covered during this leg of the journey.
Part 1: Flight from A to B
- Distance = Speed x Time
- Distance = 600 km/h x 1.5 hours = 900 km
Part 2: Flight from B to C
- Distance = Speed x Time
- Distance = 400 km/h x 1.5 hours = 600 km
Now, to find the distance from C to A and the bearing of C from A, we can use the sine and cosine rules in trigonometry.
1. Calculate the angle at airport B:
- Angle at B = 180° - (130° - 35°) = 85°
2. Use the sine rule to find the ratio between the side lengths and angles of the triangle formed by airports A, B, and C:
- Sin(Angle at A) / Distance from A to C = Sin(Angle at B) / Distance from B to C
3. Substitute the known values and solve for Distance from A to C:
- sin(85°) / Distance from A to C = sin(35°) / 600
- Distance from A to C = (sin(85°) / sin(35°)) * 600 ≈ 959.3 km
4. Use the cosine rule to find the bearing of C from A:
- Cosine rule: C^2 = A^2 + B^2 - 2AB * cos(angle)
- A = Distance from A to C = 959.3 km
- B = Distance from B to C = 600 km
- Angle = Angle at A = 35°
- C^2 = (959.3)^2 + (600)^2 - 2(959.3)(600) * cos(35°)
- Calculate C using the above equation. C ≈ 1237.4 km
5. Calculate the angle between the line from A to C and the line going north (North is 0°):
- Angle = sin^(-1)((959.3/1237.4) * sin(35°)) ≈ 21.7°
Therefore, the distance from C to A is approximately 959.3 km, and the bearing of C from A is approximately 21.7°.