In a right triangle, we define the cosine of an acute angle $\alpha$ by $\cos \alpha=\frac{\text { adjacent side }}{\text { hypotenuse }}$.

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

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-011.jpg?height=305&width=485&top_left_y=2029&top_left_x=1391)
According to the definition of cosine, we have $\cos 25^{\circ}=1 /(O M), \cos 41^{\circ}=1 /(O N)$ and $\cos 58^{\circ}=1 /(O B)$. In the figure, we see that $O M<O N<O B$. Therefore, $\cos 58^{\circ}<\cos 41^{\circ}<\cos 25^{\circ}$.