Question #232648

7.

Annett, starting from a point A, walks 8km on bearing of 2650


to a point B. From B she walks on


bearing of 1350


for 9km to a point C. Find the bearing of A from C.


1
Expert's answer
2021-09-03T15:14:39-0400

The bearing of a point is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass with the point. 


AB=(8sin(265°),8cos(265°))\overrightarrow{AB}=(8\sin(265\degree), 8\cos(265\degree))

BC=(9sin(135°),9cos(135°))\overrightarrow{BC}=(9\sin(135\degree), 9\cos(135\degree))

AC=AB+BC\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC}

=(8sin(265°)+9sin(135°),8cos(265°)+9cos(135°))=(8\sin(265\degree)+9\sin(135\degree), 8\cos(265\degree)+9\cos(135\degree))

tanθ=8cos(265°)+9cos(135°)8sin(265°)+9sin(135°)\tan \theta=\dfrac{8\cos(265\degree)+9\cos(135\degree)}{8\sin(265\degree)+9\sin(135\degree)}

The bearing of A from C


90°θ=90°tan1(8cos(265°)+9cos(135°)8sin(265°)+9sin(135°))90\degree-\theta=90\degree-\tan^{-1}(\dfrac{8\cos(265\degree)+9\cos(135\degree)}{8\sin(265\degree)+9\sin(135\degree)})

12.81°\approx12.81\degree

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS