A boat sails 50km on a bearing of 070degrees.
How far east does the boat travel?
To find out how far east the boat travels, we can use the concept of trigonometry.
First, we need to understand that the bearing of 070 degrees indicates the angle between the direction in which the boat is sailing and the north direction.
Since the boat is sailing 50 km, we can use the trigonometric function cosine to determine the distance it travels east.
Cosine is defined as the adjacent side divided by the hypotenuse in a right triangle. In this case, the adjacent side represents the distance traveled east, and the hypotenuse represents the total distance traveled by the boat, which is 50 km.
So, we can calculate the distance traveled east as follows:
East distance = 50 km * cos(70 degrees)
Using a calculator, we find:
East distance ≈ 50 km * 0.342
East distance ≈ 17.1 km
Therefore, the boat travels approximately 17.1 km east.
To find how far east the boat travels, we need to break down the given information.
The bearing of 070 degrees indicates the direction in which the boat is sailing relative to north. In this case, the boat is sailing 70 degrees clockwise from north.
Since we want to find the eastward distance, we need to consider the horizontal component of the boat's motion. Eastward movement can be represented by the X-axis in a coordinate plane.
To calculate the eastward distance, we can use trigonometry. In a right-angled triangle formed by the boat's path, the angle between the north direction and the boat's path is 20 degrees (90 degrees - 70 degrees). The hypotenuse of the triangle represents the boat's total displacement, which is given as 50 km.
We can use the cosine function to find the eastward distance (adjacent side) of the triangle:
cos(angle) = adjacent / hypotenuse
cos(20 degrees) = adjacent / 50 km
We can rearrange the equation to solve for the adjacent side (eastward distance):
adjacent = cos(20 degrees) * 50 km
Using a calculator, we can find the cosine of 20 degrees to be approximately 0.9397.
adjacent ≈ 0.9397 * 50 km
Therefore, the boat travels approximately 46.985 km (or rounded to 47 km) eastward.
50 sin70°
time to review the basic trig functions and right triangles.
And ships sail on headings, not bearings.