A painter uses a trestle to stand on in order to paint a ceiling. It consists of 2 stepladders connected by a 4 metre long plank.The inner feet of the 2 stepladders are 3 metre apart, and each ladder has slopping sides of 2.5 metres. How high of the ground is the plank?
As usual, draw a diagram.
Assuming the plank is just long enough to join the tops of the ladders, there is a 1/2 m overlap on each end, above the sloping side. So, the height is
√(2.5^2 - .5^2)
To find the height of the plank from the ground, we need to consider 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 two sides are the height of the stepladders (2.5 meters) and the distance between the feet of the stepladders (3 meters). Let's call the height of the plank "h."
Using the Pythagorean theorem, we can calculate the height of the plank:
(2.5^2) + (3^2) = h^2
6.25 + 9 = h^2
15.25 = h^2
To find "h," we need to take the square root of both sides:
h = √15.25
h ≈ 3.9 meters
Therefore, the height of the plank from the ground is approximately 3.9 meters.
To find the height of the plank from the ground, 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.
Let's call the height of the plank from the ground "h". We can set up a right-angled triangle using the height of one step ladder (2.5 meters) and the distance between the inner feet of the two step ladders (3 meters) as the other two sides.
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h | / 2.5
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Using the Pythagorean theorem, we have:
h^2 = 2.5^2 + 3^2
h^2 = 6.25 + 9
h^2 = 15.25
Taking the square root of both sides, we get:
h ≈ √15.25
h ≈ 3.91 meters
Therefore, the height of the plank from the ground is approximately 3.91 meters.