Answer:
Therefore, the height of the ladder is approximately 13.86 ft.
Explanation:
To determine the height of the ladder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
1. Given information:
Distance of the ladder from the house = 8 ft
Height of the ladder = unknown (let's call it h)
2. Apply the Pythagorean theorem:
In this case, the ladder, the distance from the house, and the height form a right triangle. The ladder is the hypotenuse, the distance from the house is one side, and the height is the other side.
Using the Pythagorean theorem:
(distance from the house)^2 + (height)^2 = (ladder)^2
(8 ft)^2 + h^2 = (16 ft)^2
64 ft^2 + h^2 = 256 ft^2
3. Solve for h:
Subtract 64 ft^2 from both sides of the equation:
h^2 = 256 ft^2 - 64 ft^2
h^2 = 192 ft^2
Take the square root of both sides to find h:
h = √(192 ft^2)
h ≈ 13.86 ft (rounded to two decimal places)