The diagram represents a triangular prism. The triangular base, $ABCD$, is horizontal. $AB=20 \mathrm{cm}$ and $BC=15 \mathrm{cm}$. The cross- section of the prism, $BCE$, is right-angled at $C$ and $\angle EBC=41°$. Calculate the length of $EC$ in $\mathrm{cm}$ correct to $1$ decimal places.

 The diagram represents a triangular prism. The triangular base, $ABCD$, is horizontal. $AB=20 \mathrm{cm}$ and $BC=15 \mathrm{cm}$. The cross- section of the prism, $BCE$, is right-angled at $C$ and $\angle EBC=41°$. Calculate the angle (in degree measure) in which the line $AE$ makes with the horizontal.

The cube shown in the diagram has sides of $5 \mathrm{m}$. Use the Pythagoras' theorem to calculate the distance $EG$. Leave your answer in exact form.

The cube shown in the diagram has sides of $5 \mathrm{m}$. Use the Pythagoras' theorem to calculate the distance $AG$. Leave your answer in exact form.

The cube shown in the diagram has sides of $5 \mathrm{m}$. Calculate the angle(in degree measure) between the line $AG$ and the plane $EFGH$. Give your answer to $1$ decimal place.

The diagram shows a tetrahedron $ABCD$. $M$ is the mid-point of $CD$. $AB=4 \mathrm{m}$, $AC=3 \mathrm{m}$, $AD=3 \mathrm{m}$. Calculate the angle $ACB.$(Give the answer in degree measure with two decimal places)

The diagram shows a tetrahedron $ABCD$. $M$ is the mid-point of $CD$. $AB=4 \mathrm{m}$, $AC=3 \mathrm{m}$, $AD=3 \mathrm{m}$. Calculate $BC$.(Give the answer in $\mathrm{m}$)

The diagram shows a tetrahedron $ABCD$. $M$ is the mid-point of $CD$. $AB=4 \mathrm{m}$, $AC=3 \mathrm{m}$, $AD=3 \mathrm{m}$. Calculate $CD$(Give the answer in $\mathrm{m}$ with two decimal places)

The diagram shows a tetrahedron $ABCD$. $M$ is the mid-point of $CD$. $AB=4 \mathrm{m}$, $AC=3 \mathrm{m}$, $AD=3 \mathrm{m}$. Calculate the length of $BM$(Give the answer in $\mathrm{m}$ with two decimal places)