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.

The diagram shows the graph of $y=\sin \left(x\right)$ for $0\le x\le 360$.

Write down the co-ordinates of $A$, the point on the graph where $x=90°$.

The diagram shows the graph of $y=\sin \left(x\right)$ for $0\le x\le 360$.

Find the value of $\sin \left(270°\right)$.

The diagram shows the graph of $y=\sin \left(x\right)$ for $0\le x\le 360$.

On a copy of the diagram, draw the line $y=-\frac{1}{2}$ for $0\le x\le 360$.

The diagram shows the graph of $y=\sin \left(x\right)$ for $0\le x\le 360$.

How many solutions are there for the equation $\sin \left(x\right)=-\frac{1}{2}$ for $0\le x\le 360$.

Two ships leave port $P$ at the same time. One ship sails $60 km$ on a bearing of $030°$ to position $A$. The other ship sails $100 km$ on a bearing of $110°$ to position $B$.

Calculate the distance $AB$

Two ships leave port $P$ at the same time. One ship sails $60 km$ on a bearing of $030°$ to position $A$. The other ship sails $100 km$ on a bearing of $110°$ to position $B$.

Calculate $\angle PAB$.

Two ships leave port $P$ at the same time. One ship sails $60 km$ on a bearing of $030°$ to position $A$. The other ship sails $100 km$ on a bearing of $110°$ to position $B$.

Calculate the bearing of $B$ from $A$.

Two ships leave port $P$ at the same time. One ship sails $60 km$ on a bearing of $030°$ to position $A$. The other ship sails $100 km$ on a bearing of $110°$ to position $B$.

Both ships took the same time, $t$ hours, to reach their $P$ positions. The speed of the faster ship was $20 km/h$. Write down the value of $t$.