A ladder 10 meters long reaches a window 8 meters high. How far is the base of the ladder from the wall?
Practice Questions
1 question
Q1
A ladder 10 meters long reaches a window 8 meters high. How far is the base of the ladder from the wall?
6 meters
4 meters
5 meters
3 meters
Using Pythagoras: base = √(10^2 - 8^2) = √(100 - 64) = √36 = 6 meters
Questions & Step-by-step Solutions
1 item
Q
Q: A ladder 10 meters long reaches a window 8 meters high. How far is the base of the ladder from the wall?
Solution: Using Pythagoras: base = √(10^2 - 8^2) = √(100 - 64) = √36 = 6 meters
Steps: 10
Step 1: Understand that the ladder, the wall, and the ground form a right triangle.
Step 2: Identify the lengths: the ladder is the hypotenuse (10 meters), the height of the window is one side (8 meters), and the distance from the wall to the base of the ladder is the other side (which we need to find).
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is c^2 = a^2 + b^2.
Step 4: In our case, let c = 10 meters (the ladder), a = 8 meters (the height), and b be the distance from the wall (which we need to find).
Step 5: Rearrange the formula to find b: b^2 = c^2 - a^2.
Step 6: Substitute the values: b^2 = 10^2 - 8^2.
Step 7: Calculate 10^2 = 100 and 8^2 = 64, so b^2 = 100 - 64.
Step 8: Simplify: b^2 = 36.
Step 9: Take the square root of both sides to find b: b = √36.
