an aeroplane leaves an airport, flies due north for 2hrs at 500km/h. It then flies on a bearing of 053 degree at 300km/h for 90mins. How far is the plane from the airport correct to 1 dp

Answer 1

use the law of cosines. The distance z is
z^2 = 1000^2 + 450^2 - 2*1000*450 cos127°

Answer 2

All angles are measured CW from +y-axis.
d1 = 500*2 = 1000km[0o].
d2 = 300*1.5 = 450km[53o].

D = d1+d2.
D = (1000*sin0+450*sin53)+(1000*cos0+450*cos53)i
D = 359.4 + 1270.8i = 1320.7km[16o].