a ship has maintained a bearing of 47 degrees. ( a bearing is the angle measured clockwise from due north)
a) how far has the ship sailed if it is 200 miles north of its original position?
b) how far east of its original position is the ship?
c) if the ship's average speed is 12 miles per hour, for how long has it been sailing?
Did you draw a diagram?
draw the path of the ship, this will be the hypotenuse, let its distance be h miles
draw the line to the y-axis
a) then cos 47º = 200/h
solve for h
b) sin 47º = x/h, where h is your result from a)
c) isn't time = distance/rate?
so time = h/12 hours
The landlubber textbook writer means a "heading", not "bearing".
Heading is the direction your vehicle is pointing.
Bearing is the direction you measure toward a target from the vehicle.
If the target is straight ahead, then the bearing is the heading. If the target is off to the side, heading is not bearing.
As for how to answer the faulty question, see reply by Reiny above.
To answer these questions, we need to use the concept of bearing and trigonometry. Let's solve each question step by step:
a) To calculate how far the ship has sailed, we can use trigonometry to find the length of the side adjacent to the angle of 47 degrees. In this case, the side adjacent to the angle represents the distance north the ship has sailed. We can use the cosine function to find this distance.
Using the formula: adjacent = hypotenuse * cos(angle)
Given:
Angle = 47 degrees
Hypotenuse = 200 miles
Using the cosine function:
adjacent = 200 * cos(47)
Calculating:
adjacent ≈ 200 * 0.682
Therefore, the ship has sailed approximately 136.4 miles north from its original position.
b) To calculate how far east the ship is from its original position, we need to find the length of the side opposite to the angle of 47 degrees. In this case, the side opposite to the angle represents the distance east the ship has sailed. We can use the sine function to find this distance.
Using the formula: opposite = hypotenuse * sin(angle)
Given:
Angle = 47 degrees
Hypotenuse = 200 miles
Using the sine function:
opposite = 200 * sin(47)
Calculating:
opposite ≈ 200 * 0.732
Therefore, the ship is approximately 146.4 miles east of its original position.
c) To calculate the time the ship has been sailing, we can use the formula: time = distance / speed.
Given:
Distance = 200 miles (distance north the ship has sailed)
Speed = 12 miles per hour
Using the formula:
time = 200 / 12
Calculating:
time ≈ 16.67 hours
Therefore, the ship has been sailing for approximately 16.67 hours.
To answer these questions, we need to use trigonometry and the concept of right triangles. Let's break down each question step by step:
a) How far has the ship sailed if it is 200 miles north of its original position?
To determine the distance sailed, we need to find the hypotenuse of a right triangle formed by the ship's journey. One leg represents the distance traveled north (200 miles), and the other leg represents the distance traveled east (which we need to find in question b).
We can use the trigonometric function sine (sin) to find the length of the hypotenuse. The formula to find the length of the hypotenuse (c) is:
c = a / sin(A)
In this case, a represents the 200 miles north, and A represents the angle measured clockwise from due north (47 degrees). So, the calculation is:
c = 200 / sin(47)
To find the value of sin(47), you can use a scientific calculator, online calculator, or table of trigonometric functions. Once you have the value, divide 200 by the sine of 47 degrees to find the distance the ship has sailed.
b) How far east of its original position is the ship?
In question a, we found the hypotenuse of the right triangle, which represents the total distance traveled by the ship. Now, we need to find the distance traveled east (the leg of the triangle).
To find the distance traveled east, we can use the trigonometric function cosine (cos). The formula to find the length of the adjacent side (b) is:
b = c * cos(A)
In this case, c represents the hypotenuse found in question a, and A represents the same angle measured clockwise from due north (47 degrees). So, the calculation is:
b = c * cos(47)
Again, use a calculator or table to find the cosine of 47 degrees, then multiply the hypotenuse (c) by this value to find the distance traveled east.
c) If the ship's average speed is 12 miles per hour, for how long has it been sailing?
To find the sailing time, we can use the equation:
time = distance / speed
In this case, the distance traveled is the hypotenuse (c) that we found in question a. Divide this distance by the ship's average speed (12 miles per hour) to calculate the time in hours that the ship has been sailing.
Remember to always check your units and make sure they are consistent throughout the calculations.