An aeronplane leaves an airport A and flies on a bearing 035 for 1.5 hours at 600 kilometers per hour to an airport B . It then flies on a bearing 130 for 1.5 hours at 400 kilometers per hour to an airport C calculate the distance from C to A, correct to the nearest kilometers.
Bearing of C from A, correct to nearest degree.
Regular
AB = 1.5 * 600 = 900 km
BC = 1.5 * 400 = 600 km
To find AC, use the law of cosines.
AC^2 - 900^2 + 600^2 - 2*900*600 cos85°
adding the vectors AB+BC, we have
900cis55° + 600cis(-40°) = 975.8 + 351.6i
That means that C is on a bearing of 90-19.8 = 70.2°
To calculate the distance from airport C to airport A, we need to break down the distance covered by the airplane into its horizontal and vertical components.
First, let's calculate the horizontal distance covered during the first leg of the journey.
Distance = Speed x Time
Distance = 600 km/h x 1.5 h = 900 km
Next, let's calculate the vertical distance covered during the first leg of the journey (since the bearing is given).
Vertical Distance = Horizontal Distance x tan(Bearing)
Vertical Distance = 900 km x tan(35°)
Now, let's calculate the horizontal distance covered during the second leg of the journey.
Distance = Speed x Time
Distance = 400 km/h x 1.5 h = 600 km
Next, let's calculate the vertical distance covered during the second leg of the journey (bearing is given).
Vertical Distance = Horizontal Distance x tan(Bearing)
Vertical Distance = 600 km x tan(50°)
Now, let's calculate the overall vertical distance covered by adding the vertical distances from both legs of the journey.
Overall Vertical Distance = Vertical Distance (first leg) + Vertical Distance (second leg)
Finally, let's calculate the overall distance from airport C to airport A using the Pythagorean theorem.
Distance from C to A = sqrt((Horizontal Distance)^2 + (Overall Vertical Distance)^2)
With the calculated values, you can find the distance from C to A and the bearing of C from A.