A ladder 7m long leans against a wall if the foot of the ladder is 2m away from the wall calculate how far up the wall the ladder reaches
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2^2 + h^2 =7^2
h^2 = 49 - 4 = 45
h =?
Hey wise guy, we were all doing that dang calculus problem down there.
To calculate how far up the wall the ladder reaches, we can use the Pythagorean theorem. The 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 forms a right-angled triangle with the wall and the ground. The ladder itself is the hypotenuse, with a length of 7m. The distance from the foot of the ladder to the wall is the base of the triangle, measuring 2m. We want to find out the height of the triangle, which represents how far up the wall the ladder reaches.
Using the Pythagorean theorem, we can set up the equation as follows:
(Height of ladder)^2 + (Distance from foot to wall)^2 = (Length of ladder)^2
Since we know the length of the ladder (7m) and the distance from the foot to the wall (2m), we can substitute these values into the equation:
(Height of ladder)^2 + (2m)^2 = (7m)^2
Simplifying further:
(Height of ladder)^2 + 4m^2 = 49m^2
To isolate the height of the ladder, we subtract 4m^2 from both sides:
(Height of ladder)^2 = 49m^2 - 4m^2
(Height of ladder)^2 = 45m^2
Now, we take the square root of both sides to find the height of the ladder:
Height of ladder = √(45m^2)
Height of ladder = √45 * √(m^2)
Height of ladder ≈ 6.71m
Therefore, the ladder reaches approximately 6.71m up the wall.