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Calculate the value of $h$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A uniform rectangular block has a square base $ABCD$ with $AB = BC = 0.4\,\text{m}$. The block’s height is $h\,\text{m}$. It stands on a rough plane inclined at $30^\circ$ to the horizontal with its base in contact with the plane. The block does not slide. It is given that the block is on the point of toppling when the diagonal $AC$ lies along a line of greatest slope.
Worked solution & mark scheme
This 3-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses Pythagoras to obtain $d = \sqrt{(0.2)^2 + (0.2)^2} = 0.2828$ or $AC = \sqrt{(0.4)^2 + (0.4)^2} = 0.56568$ (with $d = \tfrac12 AC$)” …
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