Victoria V. answered • 04/01/16
Tutor
5.0
(402)
Math Teacher: 20 Yrs Teaching/Tutoring CALC 1, PRECALC, ALG 2, TRIG
Is 0 degrees north or east?
If 0 degrees is north (as is customary in navigation), then the plane is traveling in a southwesterly direction, 40 degrees from the y-axis. So the cosine function could be used, the plane has gone 190 * 2 = 380 km in its southweterly direction.
If I could draw a triangle here the y-axis would be adjacent to the 40 degree angle that the plane makes with the y-axis. The hypotenuse of the triangle would be the 380 km from the origin (the airport) along the southwest flight path, the other leg of the triangle is horizontal to the x-axis.
The distance south of the airport is the distance along the y-axis, given by y=380 cos(40 degrees) = 291 km.
If 0 degrees is east (as is customary in math problems), then the 40 degree angle is made with the x-axis, and the distance south of the airport (the vertical leg of a right triangle whose hypotenuse is the flight path, still in a southwestern direction, and the horizontal leg of the right triangle is the x-axis.
The distance south of the airport (which I am assuming is the origin) is now the length of the vertical leg which is opposite the 40 degree angle, so a sine function will be used: y=380 sin(40 degrees) = 244 km.
Victoria V.
OK. North - so use first part of answer. Wish I could draw a triangle to show you what I mean. Draw the flight path from the origin into the 3rd quadrant so that it is a 40 degree angle left of the y-axis or a 50 degree angle below the x-axis. Draw this arrow from the origin into the southwest quadrant to be 190 * 2 = 380 km long. At the end of the 380 km, draw a line from this tip over to the y-axis. This should be a right triangle with the top vertex at the origin, coming down the distance that the airplain is SOUTH of the airport, and a horizontal line making a right angle with the y-axis connecting the y-axis to the hypotenuse (380 km flight path). Can you draw this and see what I am talking about?
Report
04/01/16
Cierra J.
04/01/16