A ship sails 400 km on a bearing of 75 degrees
To find out where the ship ends up after sailing 400 km on a bearing of 75 degrees, we can use basic trigonometry.
First, we need to understand what the bearing angle means. In navigation, a bearing represents the direction of an object or location measured clockwise from the north. So, a bearing of 75 degrees means the ship is sailing at an angle of 75 degrees clockwise from north.
To calculate the horizontal and vertical distances traveled by the ship, we can use trigonometric ratios. The cosine function relates the adjacent side of a right triangle to the hypotenuse, while the sine function relates the opposite side to the hypotenuse.
In this case, since the bearing angle is given, we can use the cosine function to find the horizontal component of the distance traveled:
horizontal distance = 400 km * cos(75 degrees)
Next, we can use the sine function to find the vertical component of the distance traveled:
vertical distance = 400 km * sin(75 degrees)
Using a calculator, you can find the values of cos(75 degrees) and sin(75 degrees), which are approximately 0.2588 and 0.9659, respectively.
Calculating the horizontal distance:
horizontal distance = 400 km * 0.2588 = 103.52 km
Calculating the vertical distance:
vertical distance = 400 km * 0.9659 = 386.38 km
So, the ship ends up approximately 103.52 km horizontally and 386.38 km vertically from its starting point.