A 6m ladder is placed against a wall with its base 2m from the wall . How high is the top of the ladder above the ground ? Round of your answer to two decimal places
Pythagorean theorem:
c² = a² + b²
given:
the ladders are long c = 6 m
base is a = 2 m
b = height of ladder above ground
b = √ ( c² - a² )
b = √ ( 6² - 2² )
b = √ ( 36 - 4 )
b = √ 32
b = 5.656854249 m
To round a number to a two decimal places, look at the number in the third decimal place.
Leave the second decimal same if the number in the third decimal is less than 5
(this is called rounding down)
Increase the second decimal by 1 if the number in the third decimal is 5 or more
(this is called rounding up)
In this case number in the third decimal is 6 so increase the second decimal by 1:
b = 5.66 m
rounded on two decimal places
How do we round out the number
To find the height of the top of the ladder above the ground, we can use the Pythagorean theorem.
The Pythagorean theorem 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 is the hypotenuse of the right-angled triangle, and the base of the ladder is one of the other two sides. The height we're looking for is the length of the remaining side.
Using the Pythagorean theorem equation, we can solve for the height:
height^2 + base^2 = ladder^2
Let's plug in the values we have:
height^2 + 2^2 = 6^2
Simplifying:
height^2 + 4 = 36
Subtracting 4 from both sides:
height^2 = 32
Taking the square root of both sides to isolate the height:
height = √32
Calculating the square root:
height ≈ 5.66
Rounding to two decimal places, the height of the top of the ladder above the ground is approximately 5.66 meters.
To find the height of the top of the ladder, we can use the Pythagorean theorem, which states that in a right 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 is the hypotenuse, the distance from the base of the ladder to the wall is one of the sides, and the height we want to find is the other side.
Let's assign some variables to make it easier to understand:
- Height of the ladder from the ground: h
- Distance from the base of the ladder to the wall: b
- Length of the ladder: L
According to the problem, the base of the ladder is 2m from the wall, so we can say b = 2m. The length of the ladder is given as 6m, so L = 6m.
Using the Pythagorean theorem, we have the equation: L^2 = b^2 + h^2
Plugging in the values we have, we get:
(6m)^2 = (2m)^2 + h^2
Simplifying the equation:
36m^2 = 4m^2 + h^2
Subtracting 4m^2 from both sides:
32m^2 = h^2
Taking the square root of both sides to solve for h:
√(32m^2) = √(h^2)
√(32) * m = h
Now, let's calculate the height of the top of the ladder:
h = √(32) * m
h ≈ 5.66 * m
Since m represents meters, we can round the answer to two decimal places:
h ≈ 5.66 meters
Therefore, the top of the ladder is approximately 5.66 meters above the ground.