Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Relationships in Space: Geometry and Trigonometry in 2D and 3D, Exercise 24: Exercise 11I

Calculate the area of the triangle with sides measuring $12\mathrm{cm}, 14\mathrm{cm}$ and $20\mathrm{cm}$.

A flagpole is supported by three wires $BA$, $BC$ and $BD$, as shown in this diagram.

Show that the triangle $ABC$ is not right angled.

A dockyard crane $ABC$, is used to unload cargo from ships. $AB=22.5\mathrm{m}, AC=48\mathrm{m}$ and angle $ABC=46°$. Find $A\hat{C}B$.

A dockyard crane $ABC$, is used to unload cargo from ships. $AB=22.5\mathrm{m}, AC=48\mathrm{m}$ and angle $ABC=46°$. Find the length of the lifting arm, $BC$.

Two security cameras are positioned on the ceiling of a gym, $10\mathrm{m}$ apart. One camera has an angle of depression of $50°$ to a point on the floor, and the other camera has an angle of depression of $60°$ to the same point. Calculate the height, $h$ metres, of the gym.

A ship leaves Shanghai on a bearing of $030°$. It sails a distance of $500 \mathrm{km}$ to Jeju. At $B$, the ship changes direction to a bearing of $100°$. It sails a distance of $320 \mathrm{km}$ to reach Nagasaki. Calculate the bearing and distance for the ship to return from Nagasaki to Shanghai.

Calculate the value of $\cos \left(A\hat{B}C\right)$ in this triangle.

Without actually calculating the size of the angle you will be able to say that $A\hat{B}C$ is obtuse using $\cos \left(A\hat{B}C\right)=\frac{-11}{24}$, explain why you are able to do this.