A LADDER IS LEANING AGAINST THE WALL. IF THE LADDER REACHES A HEIGHT OF 12M UP THE WALL AND HAS ITS FOOT 5M AWAY FROM IT ,CULCULATE THE LENGTH OF THE LADDER?
So for this you would use the Pythagorean Theorm.
The formula is a^2 + b^2 = c^2, where c is the hypotenuse of the triangle.
So if you know that the ladder reaches the height of 12m, that would be the hypotenuse in the triangle. 5m would be one of the legs in the triangle.
Therefore, calculate 5m^2 + ?^2 = 12m^2.
actually, 12 is one of the legs. The ladder is the hypotenuse. Make a diagram to see why.
Think 5-12-13 Pythagorean triple
To calculate the length of the ladder, we can use the Pythagorean Theorem, which states that in a right-angled triangle, the square 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 forms a right-angled triangle with the wall and the ground. The height of the ladder against the wall is one side of the triangle (12 meters), and the distance from the base of the ladder to the wall is another side (5 meters). The length of the ladder is the hypotenuse, which we need to find.
Let's label the sides of the triangle:
Height of the ladder (opposite the right angle): a = 12 meters
Distance from the base of the ladder to the wall: b = 5 meters
Length of the ladder (hypotenuse): c
Using the Pythagorean Theorem, we can write the equation:
a^2 + b^2 = c^2
Substituting the values:
12^2 + 5^2 = c^2
144 + 25 = c^2
169 = c^2
To find c, we can take the square root of both sides of the equation:
√169 = √c^2
13 = c
Therefore, the length of the ladder is 13 meters.