A motor boat moves in the direction N32degreeW for 3hrs. at 18miles per hour. How far north and how far west does it travel?
Did you make a sketch?
I have a right-angled triangle with hypotenuse of 54 and a base angle of 90-32 or 58°
sin 58 = y/54
y = 54sin58° = ... (the north distance)
cos58 = x/54
x = 54cos58 = .... (the west distance)
To determine how far north and how far west the motor boat travels, we can use trigonometry and simple calculations.
First, let's break down the given information:
Direction: N32°W
Time: 3 hours
Speed: 18 miles per hour
To find the distance north and west, we need to consider the speed and the time.
The direction N32°W forms an angle of 32° with the north direction.
The boat is moving at 18 miles per hour for 3 hours, which gives us a total distance of 18 x 3 = 54 miles.
To find the distance north and west, we can use trigonometric functions, specifically the sine and cosine functions.
The distance north (DN) can be calculated using the formula: DN = Distance x sin(angle)
DN = 54 miles x sin(32°) ≈ 54 x 0.529 ≈ 28.566 miles (rounded to three decimal places)
The distance west (DW) can be calculated using the formula: DW = Distance x cos(angle)
DW = 54 miles x cos(32°) ≈ 54 x 0.848 ≈ 45.792 miles (rounded to three decimal places)
Therefore, the motor boat travels approximately 28.566 miles north and 45.792 miles west.