a ship travels 8km due north then 7km on a bearing of 070 degrees

1. draw a diagram to represent the information
2. calculate the distance and bearing of the ship from its starting point

ships travel on headings, not bearings.

Anyway, you draw the diagram.

Starting from (0,0), going N puts you at (0,8)

Then, 7 km at 70° moves you another (7cos70°, -7sin70°) = (2.39,-6.58), leaving you at (2.39,1.42)

Final distance is 2.78, on a bearing of arctan(1.42/2.39) = 30.7° from (0,0)

11.50

To draw a diagram representing the information, you can use a coordinate grid or simply draw a rough sketch. Here's how you can approach it:

1. Begin by drawing a straight line in the north direction (upwards) to represent the ship's initial 8 km journey. Label this line as 8 km (or any suitable scale that you choose).

2. Starting from the end of the 8 km line, draw another line at an angle of 70 degrees to the right (clockwise) to represent the ship's 7 km journey on the bearing of 070 degrees. Label this line as 7 km.

3. Finally, connect the starting point (the origin) to the endpoint of the second line to complete the diagram. This will represent the ship's overall path.

To calculate the distance and bearing of the ship from its starting point, you can use vector addition. Let's break it down step by step:

1. Convert the displacement of each leg of the journey into Cartesian coordinates (x, y). In this case, the first leg is purely north, so its coordinates are (0, 8). The second leg involves a bearing, so we have to find its x and y components.

x = 7 * cos(70 degrees)
y = 7 * sin(70 degrees)

Calculate these values using a calculator or math software, and round to the appropriate decimal places.

2. Calculate the total displacement by adding the x and y components:

total displacement = (0, 8) + (x, y)

Add the x coordinates and the y coordinates separately. Round the values to the appropriate decimal places.

3. Calculate the distance using the Pythagorean theorem:

distance = √(x^2 + y^2)

Substitute the calculated values of x and y into the equation and calculate the square root. Round the result to the appropriate decimal places.

4. Calculate the bearing using trigonometry. The bearing is the angle measured clockwise from the north direction to the direction of the final displacement. Use the formula:

bearing = arctan(y / x)

Substitute the calculated values of x and y into the equation. Make sure to convert the result from radians to degrees and round to the appropriate decimal places.

By following these steps, you should be able to calculate both the distance and bearing of the ship from its starting point.