A ship sails 40 miles SOUTH and 15 miles EAST. Find the bearing from where it began? HELP.
make a sketch to complete a right-angled triangle in quadrant IV
tanØ = 15/40
Ø = 20.56°
using North as 0°, the bearing is 159.44°
http://www.mathsteacher.com.au/year7/ch08_angles/07_bear/bearing.htm
alternate way to state the direction is S 20.56° E
To find the bearing from where the ship began, we can use trigonometry. We'll use the tangent function.
Step 1: Visualize the ship's movement. Imagine a Cartesian coordinate plane with the origin (0,0) at the starting point of the ship. The ship sailed 40 miles south, which means it moved straight down along the y-axis to the point (0, -40). Then, it sailed 15 miles east, moving to the right along the x-axis to the point (15, -40).
Step 2: Calculate the angle. We need to find the angle between the positive x-axis and the segment connecting the starting point to the final position of the ship. Tan = opposite/adjacent, so we'll use the following formula: tan(angle) = (change in y) / (change in x). In this case, the change in y is -40 and the change in x is 15.
Step 3: Calculate the angle using the arctan function. Using a calculator or a trigonometric table, calculate the inverse tangent (arctan) of (-40/15). This will give you the angle in radians.
Step 4: Convert the angle to degrees. Convert the angle from radians to degrees, either by using a calculator or by multiplying the angle by 180/pi.
Step 5: Determine the bearing. The bearing is the angle measured clockwise from the north direction. Since the ship began by sailing south, the bearing will be 180 degrees plus the angle obtained in step 4.