Discussion
A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall.Find the distance of the foot of the ladder from the wall
Answer: C
Read the angle carefully: it is measured from the wall, not from the ground. The distance of the foot from the wall is therefore opposite that 60° angle, so sine applies.
\[ \sin 60^{\circ} = \frac{\text{distance from wall}}{\text{ladder}} \]
\[ x = 10 \sin 60^{\circ} = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3} \]
\[ x = 5 \times 1.732 = 8.66 \approx 8.65 \text{ m} \]
Assuming the angle is with the ground gives \( 10\cos 60^{\circ} = 5 \) m - which is exactly why 5 m appears among the options.
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