A pole 10 m long rests slantly against a vertical wall AB making an angle 30° with the horizontal (ground). Find how far the foot of the pole is from the wall (in metres).

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Let the pole be of length 10 m, making an angle of 30° with the horizontal ground. The pole touches the wall at point A (top), and its foot is at point C on the ground. The wall meets the ground at point B. The triangle ABC is a right triangle with AB (wall) vertical, BC (distance from wall to foot of pole) horizontal, and AC (pole) as the hypotenuse.

We are to find BC (distance from wall to foot of pole).

Given:
- Hypotenuse (AC) = 10 m
- Angle with ground ($\angle BCA$) = 30°

Using trigonometry:
cos(30°) =BC/AC

cos(30°) = BC/10

cos(30°) =$\sqrt{3}$/2
 
$\sqrt{3}$/2=BC/10

BC = 10 x $\sqrt{3}$/2 = $5\sqrt{3}$

Therefore, the foot of the pole is $5\sqrt{3}$ metres from the wall.

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