Question

Two forces with magnitudes of 6 pounds and 18 pounds are applied to an object. The magnitude of the resultant is 13 pounds. Find the measurement of the angle between the resultant vector and the vector of the 18 pound force to the nearest whole degree.

Answer 1

Answer: the angle between the resultant vector and the vector of the 18 pound is 28°

Explanation:

given that data in the question; as its interpreted in the diagram below;

from the cosine rule, we know that;

a² = b² + c² - 2bc  

so

(13)² = (6)² + (18)² - (2 × 6 × 18 ) cos∅

169 = 36 + 324 - 216cos∅

169 = 360 - 216cos∅

216cos∅ = 360 - 169

216cos∅ = 191

cos∅ = 0.8842

∅ = cos⁻¹ ( 0.8842 )

∅ = 27.8° ≈ 28°  {nearest whole number}

Therefore the angle between the resultant vector and the vector of the 18 pound is 28°