Question
A plane flies 400km west then 100km north. Find its distance and bearing from its starting point using scale drawing method
Answers
GPT 3.5
To find the distance and bearing from the starting point, we first need to create a scale drawing of the path the plane took.
Let's say we use a scale of 1cm = 100km.
First, draw a line 4cm long to represent the plane flying 400km west. Then draw a line perpendicular to the end of that line, 1cm long, to represent the plane flying 100km north.
Connect the start and end points of the lines to form a right triangle.
Now we can find the distance using Pythagoras' theorem:
Distance = sqrt((4cm)^2 + (1cm)^2)
Distance = sqrt(16 + 1)
Distance = sqrt(17) ≈ 4.123cm
Since 1cm represents 100km, the actual distance is 4.123 * 100 = 412.3km
To find the bearing, we need to find the angle the hypotenuse makes with the east direction.
We can use trigonometry to find this angle:
tan(theta) = opposite/adjacent
tan(theta) = 1/4
theta = arctan(1/4)
theta ≈ 14.04 degrees
Since the plane flew west before flying north, the bearing would be 90 degrees (east) + 14.04 degrees = 104.04 degrees.
Therefore, the plane is approximately 412.3km away from its starting point at a bearing of 104.04 degrees.
Let's say we use a scale of 1cm = 100km.
First, draw a line 4cm long to represent the plane flying 400km west. Then draw a line perpendicular to the end of that line, 1cm long, to represent the plane flying 100km north.
Connect the start and end points of the lines to form a right triangle.
Now we can find the distance using Pythagoras' theorem:
Distance = sqrt((4cm)^2 + (1cm)^2)
Distance = sqrt(16 + 1)
Distance = sqrt(17) ≈ 4.123cm
Since 1cm represents 100km, the actual distance is 4.123 * 100 = 412.3km
To find the bearing, we need to find the angle the hypotenuse makes with the east direction.
We can use trigonometry to find this angle:
tan(theta) = opposite/adjacent
tan(theta) = 1/4
theta = arctan(1/4)
theta ≈ 14.04 degrees
Since the plane flew west before flying north, the bearing would be 90 degrees (east) + 14.04 degrees = 104.04 degrees.
Therefore, the plane is approximately 412.3km away from its starting point at a bearing of 104.04 degrees.