Math Problem Statement

A ladder touches the wall 91 feet above the ground. Which measurement is closest to the height of the ladder against the wall?

OPTIONS

45.5 feet

22.8 feet

10.1 feet

9.5 feet

Solution

The ladder touches the wall 91 feet above the ground. This height of 91 feet represents the vertical distance from the ground to the point where the ladder meets the wall. Since the height of the ladder against the wall must be at least 91 feet (as it is touching the wall at that height), none of the given options is even close to 91 feet.

The correct answer isn't listed among the options provided. The correct height of the ladder should be at least 91 feet.

Do you want further details or have any questions?

Here are some related questions to expand your understanding:

  1. How can you calculate the length of a ladder if the height and the distance from the wall are known?
  2. What role does the Pythagorean theorem play in problems involving ladders?
  3. How would the length of the ladder change if it was moved closer or farther from the wall?
  4. How can you determine the angle at which the ladder is leaning against the wall?
  5. What are the safety guidelines for positioning a ladder against a wall?

Tip: When working with ladders, always double-check measurements to ensure safety and accuracy in problem-solving.

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Math Problem Analysis

Mathematical Concepts

Geometry
Trigonometry

Formulas

Pythagorean theorem: a^2 + b^2 = c^2

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 9-11