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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 $$\left( {\sqrt 3 = 1.73} \right)$$

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 $$\left( {\sqrt 3 = 1.73} \right)$$ Correct Answer 8.65 m

Height and Distance mcq solution image
Let BA be the ladder and AC be the wall as shown above.
Then the distance of the foot of the ladder from the wall = BC
Given that BA = 10 m, ∠ BAC = 60°
$$\eqalign{ & \sin {60^ \circ } = \frac{{BC}}{{BA}} \cr & \frac{{\sqrt 3 }}{2} = \frac{{BC}}{{10}} \cr & BC = 10 \times \frac{{\sqrt 3 }}{2} \cr & \,\,\,\,\,\,\,\,\,\, = 5 \times 1.73 \cr & \,\,\,\,\,\,\,\,\,\, = 8.65\,{\text{m}} \cr} $$

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