A 30 -feet ladder lean against a building, so that the angle between the ground and ladder is \( 75^{\circ} \). How high does the ladder reach up the side of the building?

To find out how high the ladder reaches up the side of the building, we can use trigonometry. Specifically, we utilize the sine function: The height can be calculated using the formula: \[ \text{Height} = \text{Ladder Length} \times \sin(\text{Angle}) \] In this case: \[ \text{Height} = 30 \text{ ft} \times \sin(75^\circ) \] Calculating that gives approximately: \[ \text{Height} \approx 30 \text{ ft} \times 0.9659 \approx 28.98 \text{ ft} \] So the ladder reaches about 29 feet up the side of the building! Using the ladder at an angle that's too steep or too shallow could lead to difficulties. Make sure to check the angle for safety—never try to lean a ladder against a surface without ensuring it’s secure! It's always good to refresh yourself on ladder safety guidelines to prevent accidents.