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Sagot :
Answer:
The distance between the diver and the shipwreck is approximately 130.76 m
Explanation:
The depth of the shipwreck below the surface of the water = 35 m
The location of the wreck = 55° South of West
The angle of depression of the wreck = 18°
The location of the diver = 27° South of East
The angle of depression of the diver = 30°
The distance of the wreck from the ship = 35 m/(sin(18°)) ≈ 113.26 m
The horizontal distance of the wreck from the ship = 35 m/(sin(18°)) × (cos(18°)) ≈ 107.72 m
The x-coordinate of the shipwreck, x₁ = 107.72 m × cos(55°) ≈ 61.79
The y-coordinate of the shipwreck, y₁ = 107.72 m × sin(55°) ≈ -88.24
The z-coordinate of the shipwreck, z₁ = -35
The distance of the diver from the ship = 35 m/(sin(30°)) = 70 m
The horizontal distance of the diver from the ship = 70 m × cos(30°) ≈ 60.62 n
The x-coordinate of the diver from the ship, x₂ = -60.62 m × cos(27°) ≈ -54.013
The y-coordinate of the diver from the ship, y₂ = 60.62 × sin(27°) ≈ -27.52
The z-coordinate of the diver from the ship, z₂ = -35
The distance between the diver and the shipwreck, 'd', is given by the distance between two points given the x, y, z coordinates as follows;
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
Therefore, we have;
d = √((61.79 - (-54.013))² + (-88.24 - (-27.52))² + (35 - 35)²) ≈ 130.76
The distance between the diver and the shipwreck, d ≈ 130.76 m.
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