A ship leaves port A and sails for 78km on a bearing of 165° to port B.How far is B south of A?
78 cos (180-165)
1007544
To determine how far port B is south of port A, we need to find the component of the 78km distance traveled in the southern direction.
First, let's understand the concept of bearings. Bearings are typically measured clockwise from the north direction. In this case, a bearing of 165° means the ship is sailing 165° clockwise from north.
To find the south component of the distance, we need to calculate the sine of the angle corresponding to the bearing. The sine of an angle can be determined using trigonometric functions.
1. Convert the bearing angle from degrees to radians:
- Since the trigonometric functions usually take radians as input, we need to convert the bearing angle in degrees to radians.
- To convert degrees to radians, multiply the degree value by (π/180) (approximately 0.01745).
- In this case, 165° * (π/180) ≈ 2.87979 radians.
2. Calculate the sine of the angle:
- Use a scientific calculator or computer tool to find the sine of the angle.
- sin(2.87979) ≈ -0.24869 (rounded to five decimal places).
The negative sign indicates that the component is in the opposite direction from the chosen reference axis.
3. Determine the south component distance:
- Multiply the sine value by the total distance traveled (78km).
- -0.24869 * 78km ≈ -19.35942km (rounded to five decimal places).
Hence, port B is approximately 19.35942km south of port A.