88.Two forces of 12 and 15 newtons act at a point. The resultant force is 25 newtons. Find the angle between the forces.

Answer 1

Let angle betwwen forces F₁= 12 N and F₂ = 15 N is θ° and resultant force is R, Then by Cosine Law

R² = F₁² + F₂² - 2F₁F₂cos(180° - θ). From here cos(180° - θ) = (F₁² + F₂² - R²)/(2F₁F₂);

180° - θ = cos^-1(( 12² + 15² - 25²)/(2·12·15)) ≅ 135.3°.

From here θ = 180° - 135.3° = 44.7°.

Answer: Angle between forces is about 44.7°.

Answer 2

You need to add 2 vectors, that means to find the diagonal of parallelogram

First we will find the supplemental angle φ using law of cosine

25² = 12² + 15² - 2*12*15* cos φ

You will get the cosφ from that equation, and the angle in question θ - is the other angle of parallelogram.

So θ = 180 - φ