A firefighter’s ladder of length 41 meters is resting against a wall and makes an angle x with the ground such that sin x = 40/41. Find the horizontal distance of the foot of the ladder from the wall.
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Correct answer: A
Explanation
Given:
Length of ladder = 41 meters
sin x = 40/41
Formula:
sin θ = opposite side / hypotenuse
cos θ = base / hypotenuse
sin²θ + cos²θ = 1
sin x = 40/41
sin²x = (40/41)² = 1600/1681
cos²x = 1 − 1600/1681 = 81/1681
cos x = 9/41
cos x = base / 41
9/41 = base / 41
base = 9