SOLUTION: A plane is flying 215 miles per hour toward the Southeast (Theta Angle is 315 degrees). A wind suddenly blows at 75 miles per hour from the North to the South (Theta Angle is 270

Question 1022497: A plane is flying 215 miles per hour toward the Southeast (Theta Angle is 315 degrees). A wind suddenly blows at 75 miles per hour from the North to the South (Theta Angle is 270 degrees). Remember you will have to find the X-components & Y-components of the plane and wind.
New velocity of plane
Angle Alpha is
Angle Theta is

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A plane is flying 215 miles per hour toward the Southeast (Theta Angle is 315 degrees). A wind suddenly blows at 75 miles per hour from the North to the South (Theta Angle is 270 degrees). Remember you will have to find the X-components & Y-components of the plane and wind.
New velocity of plane
Angle Alpha is
Angle Theta is
========================
In aviation (and other navigation) North is 0/360 degs, and angles are measured clockwise.
----
The plane's heading is 135 degs.
The wind is 360 @ 75.
---
Draw a triangle with a leg of length 215 (the speed) at 135 degs.
From the lower right end, draw a vertical line of length 75 (windspeed).
The angle between the 2 legs is 135 degs.
Use the Cosine Law to find the 3rd side (the resultant ground speed).

c =~ 273.23 mi/hr (the groundspeed)
----------------------
Call the angle between the plane's heading and its ground track A:
Use the Sine Law:
sin(A)/75 = sin(135)/273.23
sin(A) =~ 0.194
A = 11.19 degs
--> ground track = 146.19 degs
----------
Angle on the x-y plane = 303.8 degs
The ground track = 135 + angle A
===================
It's not clear what angles alpha and theta are located.
--------------------
PS Pilots don't do trig, they use computers of various types to do it for them.
RELATED QUESTIONS
A plane is flying 215 miles per hour toward the Southeast (Theta Angle is 315 degrees). A (answered by Alan3354)

A plane is flying 400 miles per hour due North (Theta Angle is 90 degrees). A wind... (answered by josgarithmetic)

#80 Air Traffic Control. An air traffic controller spots two planes at the same altitude (answered by vleith)

The distance from Parrot Point Airport to the Ivy Cliffs is 294 miles at and angle of 8.7 (answered by Alan3354)

a plane is flying due south at 310 miles per hour and the wind is blowing from east at 40 (answered by solver91311)

a plane is flying at 174 miles per hour with a heading of 50.5 degrees from due north.... (answered by Alan3354)

An airplane is headed northeast, bearing 45◦, with an air speed of 500 miles per... (answered by Alan3354)

An air traffic controller spots two planes flying at the same altitude. Their flight... (answered by mananth,ikleyn)

A plane flies at x miles per hour in still air. Flying with a tailwind, its speed is... (answered by dfrazzetto)