In this question-
A motorboat is racing towards north at 25km/h and the water current in that region is 10km/hr in the direction of 60 degree east of south. Find the resultant velocity of the boat.
The first part is quite easy and we get 21.8 approx as the magnitude of the resultant.
My doubt is in the 2nd part of the question. How do we calculate the direction using the normal method. one way is to use the sine formula and say that R/sin(a)=velocity of current/sin(alpha) where a is angle between the vectors and alpha is the angle of resultant R with the north direction. this gives us the angle with the north that is 23.4 degrees which is correct but how does one use the normal tan(alpha) method which works in questions where alpha is less that 90 or equal to 90.
By the tan(alpha) method i am referring to this formula- tan(alpha)=Asin(a)/(b+A*cos(a)) one of the book says that it is tan(alpha)=10sin120/(25+10cos120) which gives the correct answer also but i cant understand how we get this. after making a parallelogram if the angle b/w vectors is less than 90 or 90 we just extend one of the sides and get 2 right angle triangles. in this case we get only one.please explain how do we do this.