A 10-FOOT LADDER IS PLACED AGAINST A VERTICAL WALL OF A BUILDING, WITH THE BOTTOM OF THE LADDER STANDING ON LEVEL GROUND 6 FEET FROM THE BASE OF THE BUILDING. How HIGH UP THE WALL DOES THE LADDER REACH?
6^2 + h^2 = 10^2
36 + h^2 = 100
h^2 = 64
h = 8
or you can see that this is a 3 - 4 - 5 right triangle
Since this forms a right angle triangle, we can use the Pythagorean Theorem.
a^2 + b^2 = c^2
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = 8
To find out how high up the wall the ladder reaches, we can use the Pythagorean Theorem, which 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 is the hypotenuse, and the distance from the base of the building to the wall and the height along the wall form the other two sides of the right triangle.
Let's denote the height up the wall as 'x'. According to the problem, the distance from the base of the building to the wall is 6 feet, and the length of the ladder is 10 feet.
Using the Pythagorean Theorem, we can write the equation:
6^2 + x^2 = 10^2
Simplifying the equation:
36 + x^2 = 100
Subtracting 36 from both sides:
x^2 = 100 - 36
x^2 = 64
Taking the square root of both sides, we get:
x = √64
x = 8
Therefore, the ladder reaches a height of 8 feet up the wall.
To find out how high up the wall the ladder reaches, you can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the lengths of the other two sides.
In this scenario, the ladder forms the hypotenuse, and the two sides are the height it reaches on the wall (unknown) and the distance from the base of the building to where the ladder is placed (6 feet). Let's assign variables to these values as follows:
H = Height reached on the wall (unknown)
B = Distance from base of building to where the ladder is placed (6 feet)
L = Length of the ladder (10 feet)
Using the Pythagorean theorem, the equation is:
L^2 = H^2 + B^2
Plugging in the known values:
10^2 = H^2 + 6^2
Simplifying this equation:
100 = H^2 + 36
To isolate H^2, subtract 36 from both sides of the equation:
64 = H^2
To solve for H, we take the square root of both sides of the equation:
√64 = √H^2
8 = H
Therefore, the ladder reaches a height of 8 feet up the wall.