NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.3Question 15
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.3
Question. 15
A 10 m ladder leans against a vertical wall with its foot 6 m from the wall. Find the height reached on the wall.
Answer:
8 m
Detailed Answer with Explanation:
Step 1: Imagine the situation as a right-angled triangle.
- The ladder is the slant side (hypotenuse) = 10 m.
- The distance of the foot of the ladder from the wall is the base = 6 m.
- The height reached on the wall is the perpendicular side. This is what we need to find.
Step 2: Use the Pythagoras Theorem:
\[( ext{Hypotenuse})^2 = ( ext{Base})^2 + ( ext{Height})^2\]
Step 3: Substitute the values:
\[10^2 = 6^2 + ( ext{Height})^2\]
\[100 = 36 + ( ext{Height})^2\]
Step 4: Simplify:
\[( ext{Height})^2 = 100 - 36 = 64\]
Step 5: Take square root:
\[ ext{Height} = \sqrt{64} = 8\, ext{m}\]
Final Answer: The ladder reaches a height of 8 metres on the wall.