11
11​-foot ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground
7
7 feet from the base of the building. How high up the wall does the ladder​ reach?
isnt this a right triangle? a^2=c^2-b^2 ?
To determine how high up the wall the ladder reaches, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the distance from the base of the building to the ladder is one of the legs, and the height up the wall is the other leg.
Let's assign variables to the unknowns:
- Length of the ladder (hypotenuse): c (11 feet)
- Distance from the base of the building to the ladder: a (7 feet)
- Height up the wall: b (unknown)
Now we can use the Pythagorean theorem to set up the equation:
c^2 = a^2 + b^2
Plugging in the given values:
11^2 = 7^2 + b^2
Simplifying the equation:
121 = 49 + b^2
Subtracting 49 from both sides:
72 = b^2
To solve for b, we need to take the square root of both sides:
√72 = √b^2
Simplifying the square root of 72:
b = √(36 * 2)
Since 36 is a perfect square, we can simplify further:
b = 6√2
Therefore, the ladder reaches a height of 6√2 feet up the wall.