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A ladder is 16 ft talk but is leaning 8ft away from the house how tall is the ladder

User Bobjt
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7 votes

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)

User Binzo
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