Trig

The problem is: an airplane is flying in the direction 120 degrees with an airspeed of 320 mph, and a 35 mph wind is blowing in the direction 60 degrees. The question ask to find the true course and the ground speed. To solve the problem I have done this:
Flying 120sin 320_+120cos320_
Wind 60sin(35-180)_+60cos(35-180)_
I understand that I then add the together. The problem is where there are _ I don't know what direction I am suppost to put and how to determine it.

  1. 👍 0
  2. 👎 0
  3. 👁 326
asked by Morgan
  1. (320cos120 , 320sin120) + (35cos60 , 35sin60)

    you should be familiar with the trig ratios of the 30-60-90 triangle, and the multiples of those angles using the CAST rule

    = (320(-1/2) , 320(√3/2) + (35(1/2) + 35(√3/2)
    = (-160 , 160√3) + (35/2 , 35√3/2)
    =( -142.5 , 177.5√3)

    magnitude = √( (-142.5)^2 + (177.5√3)^2 )
    = appr 338.9 mph

    direction:
    tanØ = 177.5√3/-142.5 = -2.157...
    Ø = 180 - 65.13 = appr 114.9°

    I you make a sketch you will see that you could also use the cosine law,
    I got the same answer that way.

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. PreCalc - Vectors

    An airplane is flying with an airspeed of 660 Kilometers per hour. The wind is blowing from 345 degrees at 35 km/h. What direction should the airplane take so that, with the wind, the plane will be flying in a direction of 72

    asked by Joe on May 3, 2011
  2. Pre-calculus

    An airplane has an airspeed of 150 km/hr. It is to make a flight in a direction of 70 degrees while there is a 25 km/hr wind from 340 degrees. What will the airplane's actual heading be? Please Explain this Problem to me!!!!

    asked by Desperate!!!! on November 22, 2011
  3. Cartesian Vectors

    An airplane is flying at an airspeed of 345 km/h on a heading of 040 degrees. The wind is blowing at 18 km/h from a bearing of 087 degrees. Determine the ground velocity of the airplane.

    asked by Anonymous on May 24, 2010
  4. Calculus

    How would you solve this problem: An airplane is flying in still air with an airspeed of 240 mph. If it is climbing at an angle of 22 degrees, find the rate at which it is gaining altitude.

    asked by Anonymous on November 17, 2010
  5. Math

    an airplane is flying with an airspeed of 145 mph and a heading of 84.5 degrees. q wind of 24.6 omh is blowing at a heading of 68.4 degrees. find the ground speed and course of airplane

    asked by Ibrahim on April 14, 2016
  1. Precalculus

    An airplane is flying on a bearing of 285 degrees at 480 mph. A wind is blowing with the bearing 265 degrees at 30? a. find the component from of the velocity of the airplane b. find the actual speed and direction of the airplane

    asked by Anonymous on April 25, 2018
  2. trig

    An airplane has an airspeed of 450 km/hr bearing N45E. The wind velocity is 30 km/hr in the direction N30W. What is the ground speed and what is its direction?. I have gotten this far: A= 450cos(45), 450sin(45) = (318.20, 318.20)

    asked by VEJ on July 13, 2011
  3. calculus

    Multiple choice: An airplane flying due east at 539 mph in still air, encounters a 61-mph tail wind acting in the direction 45 degrees north of east. The airplane holds its compass heading but because of the wind acquires a new

    asked by lon on June 3, 2014
  4. Calculus

    An airplane is flying at 550 km/h on a heading of 080 degrees: The wind is blowing at 60 km/h from a bearing of 120 degrees. Find the ground velocity of the airplane.

    asked by Ariza on May 2, 2010
  5. Math Precal

    An airplane has an airspeed of 650 km/h bearing 15 degrees north of west. The wind velocity of is 19 km/h in the direction of 30 degrees east of south. Find the resultant vector representing the path of the plane relative to the

    asked by chris on September 6, 2016

More Similar Questions