A ladder of lent 8.1 m is propped on an horizontal ground against the vertical wall with his bottom end at a distance of 1.6 m from the wall how I up the wall is the top end. Give your answer in one decimal place.

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1. Set up the equation using the Pythagorean theorem: h^2 + 1.6^2 = 8.1^2

2. Solve for \( h \) by rearranging terms: h^2 = 8.1^2 - 1.6^2

3. Calculate each square:
8.1^2 = 65.61
1.6^2 = 2.56

4. Subtract to find the square of the height:
h^2 = 65.61 - 2.56 = 63.05

5. Find the square root to solve for \( h \):
h = \sqrt{63.05} \approx 7.9

6. Therefore, the top end of the ladder reaches approximately 7.9 meters up the wall.