Question

The resultant of two forces are 20n. one of the force is 10/√3 the angle beteen the 2 forces is 30 degrees. find the 2nd force

Answer 1

here r(resultant)=20 and a=20sqrt(3) 
angle between resultant and one of the force vector is 30 degrees

concept= since we know two sides and angle between them, we can use cosine rule to find the third side.

cosine rule for above triangle is=>
                          cos(30degrees)= ((20^2)  +   ((20sqrt3)^2)  -  b^2)/(2*20*20sqrt3)


cos(30degrees)=sqrt3/2  (substituting we get)

1200 =  1200 + 400 - b^2

b^2=400

b=20(magnitude)

for angle between this vector and resultant we proceed as follows

since r=b=20
so angle between r and a is same as angle between (-a) and b ( property of isosceles triangle)

so angle between vector b and resultant vector r is calculated as

sum of all angles of a triangle is 180 degrees

30 + 30 + (<(r,b)) = 180        ( all angles in degrees)

angle between r and b = 180 - 60 = 120 degrees