The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
9.2 m
Imagine a right-angled triangle formed by the ladder, the wall, and the ground. The angle between the ground and the ladder is 60°. The distance from the wall to the foot of the ladder (4.6 m) is the adjacent side. The length of the ladder is the hypotenuse. We use the cosine function: cos(60°) = adjacent/hypotenuse. cos(60°) = 1/2. So, 1/2 = 4.6 m / hypotenuse. Solving for the hypotenuse (ladder length): hypotenuse = 4.6 m * 2 = 9.2 m. Therefore, the length of the ladder is 9.2 m.
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