Question

Tony DiNozzo travels 15 km from A to B on a bearing of 025. He then travels due East for 24 km to C.a) Draw a diagram to illustrate his trip. Be sure to number your diagram in your work. You will upload yourwork at the end of the test.b) AC-c) Calculate the bearing of A from O.

Answer 1

a) Diagram below

b) AC = 28.3 km

1) Considering what's been given we can sketch out:

• Note that we're considering that the bearing is always taken in a clockwise direction from North.

,

• Since DiNozzo headed East then we can state the leg BC is perpendicular, therefore we have a right triangle.

b) To find out AC we need to find out at least one angle.

We can make it using some properties and trigonometric ratios.

`\begin{gathered} \tan (C)=(15)/(24) \\ C=\tan ^(-1)((15)/(24)) \\ m\angle C=32.00 \end{gathered}`

To find out the distance AC, we can write out the Law of Cosines to find this out:

`\begin{gathered} b^2=a^2+c^2-2ac\cdot\cos (B) \\ b^2=15^2+24^2-2\cdot15\cdot_{}24\cdot\cos (90) \\ b^2=225+576-0 \\ b^2=801 \\ \sqrt[]{b^2}=\sqrt[]{801} \\ b=28.30 \end{gathered}`

3) Hence, the distance of AC, i.e. b, is 28.3 km approximately 28 km