IDNLearn.com: Your trusted source for accurate and reliable answers. Join our community to receive prompt and reliable responses to your questions from experienced professionals.
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.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.