Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 11.3

The pair of given triangles are similar. Calculate the unknown length in $\mathrm{m}$.

The pair of given triangles are similar. Calculate the unknown length in $\mathrm{cm}$. (Round off the answer to one decimal place)

The diagram shows triangle $ABC$. If $AC$ is parallel to $EF$, find the length of $AC$ in $\mathrm{cm}$. (Round off answer to one decimal place)

In the diagram $AB$ is parallel to $DE$. Find the length of $CE$ in $\mathrm{cm}$.

The diagram shows a part of a children's climbing frame. Find the length of $BC$. (Round off answer to one decimal place)

Swimmer $A$ and boat $B$, shown in the diagram, are $80 \mathrm{m}$ apart, and boat $B$ is $1200 \mathrm{m}$ from the lighthouse $C$. The height of the boat is $12 \mathrm{m}$ and the swimmer can just see the top of the lighthouse at the top of the boat's mast when his head lies at sea level. What is the height of the lighthouse?

The diagram shows a circular cone that has been filled to a depth of $18 \mathrm{cm}$. Find $r$ if the radius of the top of the cone is $r \mathrm{cm}$.

The diagram shows a stepladder that is held in place by an $80 \mathrm{cm}$ piece of wire. Find $x$ in $\mathrm{cm}$.