A ladder 25 feet long is leaning against a wall the bottom of the latter is 4 feet from the base of the wall how far up is the is the top of the ladder round to the nearest 10th if necessary

Answer: the top of the ladder is 24.7 ft from the ground.

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height, h from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the the height, h that the ladder reaches, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

25² = h² + 4²

625 = h² + 16

h² = 625 - 16 = 609

h = √609

h = 24.7 ft

The answer to your question is 24.7 ft

Step-by-step explanation:

Data

length of the ladder = 25 ft

distance from the ladder to the ladder = 4 ft

distance from the floor to the ladder = ?

Process

1. - Use the Pythagorean theorem to solve this problem

c² = a² + b²

- solve for b

b² = c² - a²

-Substitution

b² = (25) ² - (4) ²

-Simplification

b² = 625 - 16

b² = 609

-Result

b = 24.67 ft ≈ 24.7 ft

-Conclusion

The ladder is 24.7 ft from the floor.