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Home » z = c \sin(\phi) \cos(\phi) - High Altitude Science

z = c \sin(\phi) \cos(\phi) - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 In a right triangle, one leg is 6 cm longer than the other, and the hypotenuse is 15 cm. What is the length of the shorter leg?

📌 Let the shorter leg be \( x \). Then the other leg is \( x + 6 \).

📌 \( x^2 + (x + 6)^2 = 15^2 \)

📌 Expand: \( x^2 + x^2 + 12x + 36 = 225 \)

📌 Combine: \( 2x^2 + 12x + 36 = 225 \)

📌 Subtract 225: \( 2x^2 + 12x - 189 = 0 \)

📌 Divide by 2: \( x^2 + 6x - 94.5 = 0 \)

📌 \( x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-94.5)}}{2} = \frac{-6 \pm \sqrt{36 + 378}}{2} = \frac{-6 \pm \sqrt{414}}{2} \)

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