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Home » Question: A historical astrolabe features a right triangle - ToelettAPP

Question: A historical astrolabe features a right triangle - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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ho \sin\phi \cos heta, \quad y =
ho \sin\phi \sin heta, \quad z =
ho \cos\phi
Substitute \(
ho = c \sin(\phi)\) into the expressions:
x = c \sin(\phi) \cdot \sin(\phi) \cos heta = c \sin^2(\phi) \cos heta
y = c \sin^2(\phi) \sin heta
z = c \sin(\phi) \cos(\phi)
Now compute \(x^2 + y^2\):
x^2 + y^2 = c^2 \sin^4(\phi) (\cos^2 heta + \sin^2 heta) = c^2 \sin^4(...

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