A plane is heading due south w/ an airspeed of 350mph. A wind in the direction of 27 degrees is blowing at 45mph. Find true course of plane.

Question

bearongs are measured north, clockwise. Round result to hundredths place.

Answer 1

airrplane speed 350 mph due south

wind blowing north 27 degrees east at 45 mph

what is true speed and direction of the plane??

wind seems to be slowing the plane down a little, not as much as 45 mph less, close though

and the wind is blowing the plan more to the South East, just a little east of south

construct a parallelogram, sides 350 and 45, angles 27 and 180-27 = 153 degrees

find the diagonal length = d = sqrd^2

use law of cosines

d^2 =350^2 + 45^2 -2(350)(45)cos27

=122,500 +2,025 - 31,500cos26

= about 124,525 - - 13809

= about 110,716

d=sqr110716= about 333 mph = plane's true speed going a little east of due south

use law of sines to find the angle

sinA/46= sin27/333

A = arcsin(46sin27/333)= about 4 degrees

plane is going 4 degrees east of due south