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MathNet 2006 — Part 02 Question 163

Math Olympiad Vault · MathNet 2006 — Part 02

Question 163

In a right-angled triangle, we define the cosine of its acute angles $\alpha$ by: $\cos \alpha=\frac{\text{adjacent leg}}{\text{hypotenuse}}=\frac{c}{a}$.

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The right triangle in the figure has side $OA=1$. Write in ascending order the cosines of the angles of $25^{\circ}, 41^{\circ}$ and $58^{\circ}$

Question illustration