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Question

An 80 m long ladder is leaning against a wall making an angle of 45° with the ground. Find the distance of the foot of the ladder from the wall.

The correct answer is

40√2 m

The problem involves determining the horizontal distance between the foot of the ladder and the wall, given the length of the ladder and the angle it makes with the ground. We can solve this using trigonometry. Consider the right triangle formed by the ladder (hypotenuse), the wall (opposite side), and the ground (adjacent side).
The given values are:
  • Length of the ladder (hypotenuse) = 80 m
  • Angle with the ground = 45°
To find the distance of the foot of the ladder from the wall (adjacent side), we use the cosine function:
cos θ = adjacent/hypotenuse
Substituting the known values:
cos 45° = adjacent/80
We know that cos 45° = 1/√2, so we can rewrite the equation:
1/√2 = adjacent/80
Cross-multiply to solve for the adjacent side:
adjacent = 80/√2
To rationalize the denominator, multiply numerator and denominator by √2:
adjacent = (80 × √2)/(√2 × √2)
The denominator simplifies to 2, so:
adjacent = (80√2)/2
Finally, dividing 80 by 2 gives:
adjacent = 40√2
Therefore, the foot of the ladder is 40√2 m from the wall.
Correct Answer40√2 m
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