Vectors based problem

Question

The angle between two vector of magnitude 12 and 18 units when the resultant is 24 units

A) 63 degree 57 min

B) 75degree 52 degree

C) 82 degree 3min

D) 89degree 16min

Is there is way to find the uncommon degrees in maths or it is only possible by using calculatator ????

Answer 1

Correct option is (B) 75.52 degree

Explanation:

As we know that
R² = A² + B² + 2ABcos(θ)
24² = 12² + 18² + 21218cos(θ)
62(4²) =62 (2² + 3² + 223cos(θ))
Cos θ = 3/12 = 0.25
we can only tick the value by graph of cosθ if there is greater difference of angle in options otherwise use calculator.

θ = 75.52 degree.