The Other Acute Angle

The known angle is not always at the corner you expect. Read every side again from the angle that has a value. In the triangle below the angle of 25° is at B, at the top, so for this problem the side AC is opposite and BC is adjacent.

y touches the 25° angle, so $\cos\left(25^{\circ}\right) = \frac{y}{10}$ and $y = 10\cos\left(25^{\circ}\right)$, about 9.06. There is a second route: the angles of a triangle add to 180°, so the angle at A is 65°, and y is opposite it, so y = 10 sin 65° gives the same 9.06. Both are right; reading the sides from the angle you were given saves a step.