A cuboid is $14 \mathrm{cm}$ long, $5 \mathrm{cm}$ wide and $3 \mathrm{cm}$ high. Calculate the length of its longest diagonal.(Give the answer in $\mathrm{cm}$ with two decimal places)

$ABCD$ is a tetrahedral drinks carton. Triangle $ABC$ is the base and $B$ is a right angle. $D$ is vertically above $B$. And $AB=BC=6 \mathrm{cm}, BD=8 \mathrm{cm}$. Calculate length of $AC$.

$ABCD$ is a tetrahedral drinks carton. Triangle $ABC$ is the base and $B$ is a right angle. $D$ is vertically above $B$. And $AB=BC=6 \mathrm{cm}, BD=8 \mathrm{cm}$. Calculate length of $DC$.

The diagram shows the cross-section of the roof of Mr Haziz's house. The house is $12 m$ wide, angle $CAB=35°$ and angle $ACB=90°$.

Calculate the lengths of the two sides of the roof, $AC$ and $BC$.

The diagram shows a trapezium $ABCD$ in which angles $ABC=BCD=90°$. $AB=90 mm, BC=72 mm \text{and} CD=25 mm$.

Calculate the angle $DAB$.

A girl, whose eyes are $1.5 m$ above the ground, stands $12 m$ away from a tall chimney. She has to raise her eyes $35°$ upwards from the horizontal to look directly at the top of the chimney.

Calculate the height of the chimney.

The diagram shows the cross-section, $PQRS$, of a cutting made for a road. $PS$ and $QR$ are horizontal. $PQ$ makes an angle of $50°$ with the horizontal.

Calculate the horizontal distance between $P$ and $Q$ (marked $x$ in the diagram).

The diagram shows the cross-section, $PQRS$, of a cutting made for a road. $PS$ and $QR$ are horizontal. $PQ$ makes an angle of $50°$ with the horizontal.

Calculate the angle which $RS$ makes with the horizontal (marked $y$ in the diagram).

A game warden is standing at a point $P$ alongside a road which runs north-south. There is a marker post at the point $X$, $60 m$ north of his position. The game warden sees a lion at $Q$  on a bearing of $040°$ from him and due east of the marker post.

Show by calculation that the distance, $QX$, of the lion from the road is $50.3 m$, correct to $3$ significant figures.