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Home » A: $\sin 65^\circ + \sin 15^\circ$ - go-checkin.com

A: $\sin 65^\circ + \sin 15^\circ$ - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \mathbf{a} \times (\mathbf{v} \times \mathbf{a}) = \mathbf{a} \times \mathbf{b}

📌 Using the identity $ \mathbf{a} \times (\mathbf{v} \times \mathbf{a}) = (\mathbf{a} \cdot \mathbf{a})\mathbf{v} - (\mathbf{a} \cdot \mathbf{v})\mathbf{a} $, and since $ \mathbf{a} \cdot \mathbf{v} = 0 $, this becomes:

📌 \|\mathbf{a}\|^2 \mathbf{v} = \mathbf{a} \times \mathbf{b}

📌 Compute $ \|\mathbf{a}\|^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 $

📌 Now compute $ \mathbf{a} \times \mathbf{b} $:

📌 \mathbf{a} \times \mathbf{b} = \begin{vmatrix}

📌 & -2 & 1 \\

📌 \end{vmatrix} = \mathbf{i}(2 \cdot 1 - 3 \cdot (-2)) - \mathbf{j}(1 \cdot 1 - 3 \cdot 1) + \mathbf{k}(1 \cdot (-2) - 2 \cdot 1)

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But let's do:
× 1.8 = 153.86 × (1 + 0.8) = 153.86 + 123.088 = 276.948 → rounds to 27...
× 1.8 = 276.948 → rounds to 277
But in exact terms, not rounded — but problem says estimated, so round...
Alternatively, compute exactly:
× 49 × 1.8 = 3.14 × 88.2 = let's compute:
× 88 = 276.32, 3.14 × 0.2 = 0.628, total 277.048 → even closer to 277....
But to match format, and since variance is small, but best:
Final answer: 277
But wait — 3.14 × 49 = 153.86, ×1.8 = 276.948 → if to nearest whole, 2...

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