the engines of a plane are pushing it due north at a rate of 300 mph, and the wind is pushing the plane 20 degrees west of north at a rate of 40 mph. what is the magnitude of the resultant vector

Answer 1

Draw and label a diagram - vectors tail to tip

Law of Cosines

m² = 300² + 40² - 2(300)(40) cos 160°

Answer 2

Liliajo

If you draw a picture of this you end up with a triangle, one side is the 300, the other is the 40, and there is a 160 degree angle between these two sides (the 160 = 180 - 20).

You need to find the side opposite the 160 degree angle.

Use the cosine rule : a²=b²+c²- 2bc cos A. a is the unknown side, b = 40, c = 300, A = 160 degrees.

(left to you to finish).

Your initial data (300, 20, 40) all have 1 significant figure, so you should round your calculated answer to one significant figure also.

Mike