Answer:
Correct answer: Vr = 87.46 yards and direction θ = 23.67° North of West
Explanation:
We obtain the required resultant position vector using the cosine theorem:
Vr² = V₁² + V₂² - 2 · V₁ · V₂ · cos α
where the vector V₁ = 72 yards and the vector V₂ = 52 yards and the angle between them is 85°
Vr² = 75² + 52² - 2 · 75 · 52 · cos 85° = 5,625 + 2,704 - 7,800 · 0.087
Vr² = 8,329 - 679.81 = 7,649.19 ⇒ Vr = √7,649.19 = 87.46 yards
Vr = 87.46 yards
The desired direction of the resultant position vector will be obtained using the sine theorem. It is in fact the angle that builds the resultant vector with the west direction.
The formula for a sine theorem is:
a / sin α = b / sin β ⇒ 87.46 / sin 85° = 52 / sin x° ⇒
sin x° = 52 · sin 85°/ 87.46 = 0.59 ⇒ x = sin⁻¹ 0.59 = 36.32°
We finally get the angle we want, we can call him θ :
θ = 60° - 36.32 = 23.67°
θ = 23.67° North of West
God is with you!!!
