A ship sales for 60km on bearing 040 degrees. How far north of it is the starting point?
The starting point is not north of it.
I assume you meant to ask "How far north of the starting point is it?"
If you draw the diagram, you should see that it is
60 cos40°
To find the distance north of the starting point, we need to break down the movement of the ship into its northward and eastward components.
First, let's consider the northward component of the ship's movement. We can find this by using trigonometry, specifically the sine function. The angle between the ship's bearing and the north direction is 90 degrees minus 40 degrees (since the bearing is measured clockwise from the north). Therefore, the northward component is:
Northward component = Distance * sin(angle)
= 60 km * sin(90 - 40)
= 60 km * sin(50 degrees)
Using a calculator, we can find that sin(50 degrees) is approximately 0.7660. So, the northward component is:
Northward component = 60 km * 0.7660
= 45.96 km
Therefore, the ship is approximately 45.96 km north of its starting point.
To find out how far north of the starting point the ship is, we need to calculate the northward distance traveled by the ship.
The bearing of 040 degrees indicates the direction in which the ship is moving. In this case, 040 degrees means the ship is moving slightly northeastward.
To calculate the northward distance, we can use trigonometry, specifically the sine function.
The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle (in this case, the northward distance) to the length of the hypotenuse (in this case, the total distance traveled by the ship).
To find the northward distance, we'll use the following steps:
Step 1: Convert the distance traveled by the ship from kilometers to meters. This will help us maintain consistency with the trigonometric calculations.
60 km = 60,000 meters.
Step 2: Calculate the northward distance using the sine function.
sine(040 degrees) = northward distance / 60,000 meters.
To find the value of the sine of 040 degrees, you can use a calculator or lookup tables.
sine(040 degrees) ≈ 0.64279 (rounded to 5 decimal places).
Now we can rearrange the equation to solve for the northward distance:
northward distance = sine(040 degrees) * 60,000 meters.
northward distance ≈ 0.64279 * 60,000 meters.
northward distance ≈ 38,566.4 meters.
Therefore, the ship is approximately 38,566.4 meters north of its starting point.