4) A ladder, 5 m long, leans against a wall. It makes an angle of \( 60^{\circ} \) with the horizontal ground. Calculate how far up the wall the ladder reaches.

To find out how far up the wall the ladder reaches, we can use trigonometry. Specifically, we can use the sine function, which relates the angle, the opposite side, and the hypotenuse of the right triangle formed by the ladder. The height \( h \) reached by the ladder can be calculated using the formula: \[ h = L \cdot \sin(\theta) \] where \( L \) is the length of the ladder (5 m) and \( \theta \) is the angle (60°). Now calculating: \[ h = 5 \cdot \sin(60^{\circ}) = 5 \cdot \frac{\sqrt{3}}{2} \approx 5 \cdot 0.866 = 4.33 \text{ m} \] Thus, the ladder reaches approximately 4.33 meters up the wall. But wait! Here’s the fun bit: imagine this ladder being used in a cartoon where a clumsy character tries to reach a cookie jar at the top of a tall cupboard. With a ladder that height, reaching for those cookies might just be an adventure! Keep your balance, or you might just end up in a cookie crumb disaster! 🍪😄