What is the length of vector A-B?

Vector A points along the y-axis with length 5.0, vector B makes an angle of 55° with respect to the x-axis and has a length of 7.0. What is the length of vector A-B?
Solution:
Aₓ=0
Ay=5
Bₓ=7cos55°
By=7sin55°
(A-B)ₓ=-7cos55°
(A-B)y=5-7sin55°
|(A-B)| = √{(-7cos55°)²+(5-7sin55°)²}
Calculation in Google calculator
sqrt((7*cos(55degree))^2+(5-7*sin(55degrees))^2)=4.0815875465
|(A-B)|≈4.1

Trigonometrical Solution:
In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states
c² = a² + b² - 2ab∙cos γ
where γ denotes the angle contained between sides of lengths a and b and opposite the side of length c.
The vector (A-B) geometrically looks as the third side of the triangle built by two vectors A and B.
|(A-B)|=√{A+B-2|A||B|cos(γ)},
where |A|=5, |B|=7, γ is the angle between vector, γ=90°-55°=35
Calculation:
sqrt(7^2+5^2-2*7*5*cos(35degree))=4.0815875465
|(A-B)|≈4.1

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