A plane, capable of flying at 190 mph with no wind, is moving at full speed in a gale blowing 103 mph from the

Question

A plane, capable of flying at 190 mph with no wind, is moving at full speed in a gale blowing 103 mph from the west. The plane's ground speed is measured at 246 mph. What direction is the plane moving relative to the ground? (Give angle in degrees relative to an axis pointing east.)

i need for review thanks

Answer 1

Let OP be the speed and direction of the plane without wind.
So OP = 190

Let PA = wind blowing to the east (fromt he west)
PA = 103 and its vector points to the east.

SO OA is the actual speed and direction of the plane
OA = 246

We are required to find the angle OA makes with the east, or the angle OAP of the triangle.
Using cosine rule:
190^2 = 103^2 + 246^2 - 2*103*246*cos(x)
cos(x) = 0.6912
x = 46.28 degrees

Answer 2

I see you didn't pay attention in math class that day.

Go look in your book under vectors.