A stick which is 11 m long lies against the wall and reaches a height of 4 m from the ground. How far from the wall is the foot of the stick? Give non-exact numerical answers correct to 3 significant figures
Question
A stick which is 11 m long lies against the wall and reaches a height of 4 m from the ground. How far from the wall is the foot of the stick? Give non-exact numerical answers correct to 3 significant figures
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right 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 lengths of the other two sides.
Here, the stick forms a right triangle with the wall and the ground. The length of the stick is the hypotenuse, the height it reaches on the wall is one side of the triangle, and the distance from the wall to the foot of the stick is the other side.
We can denote:
- c as the length of the stick (hypotenuse) = 11 m
- a as the height it reaches on the wall = 4 m
- b as the distance from the wall to the foot of the stick, which we are trying to find.
According to the Pythagorean theorem:
c² = a² + b²
We can rearrange this to solve for b:
b² = c² - a²
Substituting the given values:
b² = 11² - 4² b² = 121 - 16 b² = 105
To find b, we take the square root of 105:
b = √105
Rounding to three significant figures, b ≈ 10.2 m.
So, the foot of the stick is approximately 10.2 m from the wall.
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