Final answer:
To find the height of the top of the ladder leaning against a building, use the Pythagorean theorem to determine the length of the ladder. Plug the values into the formula and solve for the height. The height of the top of the ladder is approximately 8.7 meters.
Step-by-step explanation:
To find the height of the top of the ladder, we can use the Pythagorean theorem. The ladder, the building, and the ground form a right triangle. The ladder acts as the hypotenuse, the distance from the building is one side, and the height of the top of the ladder is the other side. We can use the formula a^2 + b^2 = c^2, where a and b are the lengths of the sides and c is the length of the hypotenuse.
In this case, the distance from the building is 5 meters and the length of the ladder is 10 meters. Plug these values into the formula: 5^2 + b^2 = 10^2. Solve for b: 25 + b^2 = 100. Subtract 25 from both sides: b^2 = 75. Take the square root of both sides to find b: b = √75 ≈ 8.7. Therefore, the height of the top of the ladder is approximately 8.7 meters.