A deer hunter tracks a deer she shot for 75 yards at 60° North of West. From this point, She tracks the deer 35° south of west for 52 yards. She needs to text the location Get help from her hunting party, what is the resultant vector and direction to her location from the starting point?

Correct  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!!!

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