To solve the problem, we will use the Pythagorean theorem. The ladder forms a right triangle where:

• The hypotenuse is the ladder length: $5.5 \, \text{m}$,
• The base (horizontal distance from the wall): $1.5 \, \text{m}$,
• The height (vertical distance from the ground to the top of the ladder): to be calculated.

Step-by-Step Solution:

1. Pythagorean theorem: $(\text{Height})^2 + (\text{Base})^2 = (\text{Ladder length})^2$ Substituting the known values: $(\text{Height})^2 + 1.5^2 = 5.5^2$

2. Simplify the equation: $(\text{Height})^2 + 2.25 = 30.25$

3. Solve for the height squared: $(\text{Height})^2 = 30.25 - 2.25$ $(\text{Height})^2 = 28$

4. Find the height: $\text{Height} = \sqrt{28}$ $\text{Height} \approx 5.3 \, \text{m} \, \text{(to one decimal place)}.$

Final Answer:

The top of the ladder is approximately 5.3 meters above the ground.

Would you like more details on any part of the solution, or do you have additional questions?

Related Questions:

1. How do you determine which trigonometric method to use for right triangle problems?
2. Can this method be applied if the base or hypotenuse length is unknown instead?
3. What is the difference between using trigonometry and the Pythagorean theorem in such problems?
4. How can we verify the answer using a calculator?
5. Are there any practical considerations to ensure safety when using ladders at such angles?

Tip:

Always check whether the given data aligns with a right triangle before applying the Pythagorean theorem.