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.

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.

Another lion appears at $R$, $200 m$ due east of the first one at $Q$.

Write down the distance $XR$.

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.

Another lion appears at $R$, $200 m$ due east of the first one at $Q$.

Calculate the distance, $PR$, of the second lion from the game warden.

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.

Another lion appears at $R$, $200 m$ due east of the first one at $Q$.

Calculate the bearing of the second lion from the game warden, correct to the nearest degree.

In the triangle $OAB$, angle $AOB=15°$, $OA=3 m$ and $OB=8 m$. Calculate, correct to $2$ decimal places the length of $AB$

In the triangle $OAB$, angle $AOB=15°$, $OA=3 m$ and $OB=8 m$. Calculate, the area of triangle $OAB$.

A pyramid, $VPQRS$, has a square base, $PQRS$, with sides of length $8 cm$. Each sloping edge is $9 cm$ long.

Calculate the perpendicular height of the pyramid.

A pyramid, $VPQRS$, has a square base, $PQRS$, with sides of length $8 cm$. Each sloping edge is $9 cm$ long.

Calculate the angle the sloping edge $VP$ makes with the base.