Pre Calculus

Question

A force of 50 pounds is directed 30 from the horizontal, find the vector that represents this force

Answer 1

Draw a right triangle with one side lying on the positive x axis and its hypotenuse along the terminal side of an angle 30^o (this angle is in Quadrant I).  Draw the vertical leg of the right triangle.

 

Because of 30-60-90 triangle, the hypotenuse is proportional to 1, the vertical leg is proportional to ½ (because across from 30 degree angle, and the horizontal leg is proportional to ½√3.

 

It seems that force F corresponds to the terminal side of the angle, so the component form of the vector F is <25√3,25>