Question
A ladder is leaning against a wall, making an angle of
60° with the ground. The top of the ladder reaches a window 15 meters above the ground. Find the length of the ladder, and also determine how far the base of the ladder is from the wall.Solution
Let the length of the ladder be L meters, and the base distance from the wall be d meters. From the triangle: sin 60° = Opposite/Hypotenuse = 15/L. √3/2 = 15/L. L = 15 × 2/√3 = 30/√3 = 10√3 m. cos 60° = Adjacent/Hypotenuse = d/L. 1/2 = d/(10√3). d = 15/√3 = 5√3 m. Correct answer: d) Length = 10√3 m, Distance = 5√3 m
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