A plane flies 400km west then 100km north. Find its distance and bearing from its starting point using scale drawing method

Answer 1

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.