contestada

The bottom of Sam's 30-foot ladder is 6 feet from the base of the wall it is
leaning against. If Sam moves the bottom of the ladder 1 foot farther away
from the wall, which of the listed statements is true?

Respuesta :

Edufirst

Answer:

  • the top of the ladder will be about  0.2 ft lower.

Explanation:

The statements are missing but I can explain you the situation to understand which conclusion can you draw about it:

When the ladder is leaning against a wall, it, the wall and the ground form a right triangle.

See the figure attached showing it:

The lenght of the ladder, 30 feet, is the hypotenuse the right triangle

When the bottom of the ladder is 6 feet from the base, the height of the point at which the ladder touches the wall can be determined using the Pythagorean theorem:

  • (30 ft)² = (6 ft)² + x²
  • x² = 900ft² - 36ft²
  • x² = 864ft²
  • x ≈ 29.4ft

When the bottom of the ladder is moved 1 foot farther away of the hypotenuse of the new righ triangle is still 30ft but the horizontal leg now is 7ft + 1ft = 8ft.

As consequence, the top of the ladder touching the wall will be lower than before. The new height of the point at which the ladder touches the wall can be determined, again, using the Pythagorean theorem:

  • x² = (30f)² - (7ft)²
  • x² = 900ft² - 49ft²
  • x² = 851ft²
  • x ≈ 29.2 ft

Those you conclude that:

  • the top of the ladder will be about 29.4ft - 29.2 ft = 0.2 ft lower.
Ver imagen Edufirst

Otras preguntas