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    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.
    A Length = 30 m, Distance = 15 m Correct Answer Incorrect Answer
    B Length = 25√3 m, Distance = 12.5 m Correct Answer Incorrect Answer
    C Length = 15√3 m, Distance = 7.5 m Correct Answer Incorrect Answer
    D Length = 10√3 m, Distance =5√3 m Correct Answer Incorrect Answer

    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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