Rose Harrison and Clara Huizink Solutions for Exercise 13: Practice 5

Find the angle $\theta$.

Find the distance $m$ in the diagram.

Find the heights from the ground of $A, B$ and $C$.

Find the side length $x$ in this diagram.

A single engine private plane flies due North for an hour and $18$ minutes at an average speed of $110 \mathrm{km}/\mathrm{h}$. It then turns and flies at the same average speed for an hour and a half on a bearing of $130°$. At the end of this time, determine how far the plane has travelled. [Enter the value excluding units]

A single engine private plane flies due North for an hour and $18$ minutes at an average speed of $110 \mathrm{km}/\mathrm{h}$. It then turns and flies at the same average speed for an hour and a half on a bearing of $130°$. At the end of this time, determine its bearing from its initial position.

Two ships leave port at $10:00$ and each one travels on a straight line course. The first one travels on a bearing of $60°$ at $23 \mathrm{km}/\mathrm{h}$ and the second one travels on a bearing of $115°$ at $28 \mathrm{km}/\mathrm{h}$. Determine how far the two ships are from one another at $12:00$ noon.

A lookout post is on top of a hill that is $100 \mathrm{m}$ above sea level. From the base of the lookout post, the angle of depression of a boat out at sea is $30°$, and from the top of the lookout post, the angle of depression of the boat is $60°$. Find the height of the lookout post. [Enter the value excluding units]