Question 1201614: An airplane flies 200 km on a bearing of 335°. It then flies 100 km on a bearing of 170° and 400 km on 280°, and lands.
a) How far is the airplane from its starting point when it lands?
b) On what bearing could it have flown to complete its journey directly?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! An airplane flies 200 km on a bearing of 335°. It then flies 100 km on a bearing of 170° and 400 km on 280°, and lands.
a) How far is the airplane from its starting point when it lands?
b) On what bearing could it have flown to complete its journey directly?
------------------------------
Label the starting point A, then B, then C, then D.
AB = 200 at 125 degs wrt the x-axis.
x component = 200*cos(125)
y component = 200*sin(125
===
BC = 100 at 280 degs wrt the x-axis.
x component = 100*cos(280), y component = 100*sin(280)
===
CD = 400 at 170 degs wrt the x-axis
x component = 400*cos(170), y component = 400*sin(170)
==================
Add the x-comps and the y-comps to find the point D
Find the distance and angle from the Origin to D.
----------------------
An Excel sheet can be used to do this.
PS To convert headings to degs wrt the x-axis, use 450 degs minus the heading MOD 360.
PPS You can waste your life doing this one with triangles. Use vectors.
|
|
|
