a ladder 20m long rest against a vertical wall so that the foot of the ladder is 9m from the wall
so what?
how high is it maybe?
81 + h^2 = 400
h^2 = 319
h = 17.9
To solve this problem, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 represents the hypotenuse, the distance from the wall to the foot of the ladder represents one side, and the height of the ladder against the wall represents the other side.
Let's call the height of the ladder h. According to the problem, the distance from the wall to the foot of the ladder is 9m, and the length of the ladder is 20m. We can use the Pythagorean theorem to find the height of the ladder:
h^2 + 9^2 = 20^2
Simplifying the equation:
h^2 + 81 = 400
Subtracting 81 from both sides:
h^2 = 400 - 81
h^2 = 319
Now we can take the square root of both sides to find the height of the ladder:
h = sqrt(319)
Approximating the square root of 319, we find:
h ≈ 17.88
So the height of the ladder against the wall is approximately 17.88 meters.