Final answer:
To determine how high the ladder reaches, we use trigonometry, particularly the cosine function, as the ladder forms a right triangle with the building. By calculating cos(80°) × 23 feet, we find the height the ladder reaches on the building.
Step-by-step explanation:
Finding the Height Reached by the Ladder on the Building
To answer the student's question, we need to use trigonometry to find out how high the ladder reaches up the side of the building. Given that the ladder is leaning at an angle of 80 degrees with the ground and the length of the ladder is 23 feet, we can apply the cosine function to solve for the height it reaches.
The height (h) can be calculated using the following trigonometric relationship:
cos(θ) = adjacent / hypotenuse
cos(80°) = height / 23 ft
height = cos(80°) × 23 ft
After calculating this using a calculator, we can find the precise height that the ladder reaches on the building. Remember that trigonometric functions use angles in degrees, so ensure your calculator is in the correct mode.
It's essential to understand that the principles of trigonometry and statics are fundamental to solving real-world problems involving angles and forces, as illustrated in the various scenarios provided, where the concept of torque and static equilibrium is applied.