Question

Could someone pls solve this bearings question?

An aeroplane flies from airport A to airport B 80 km away on a bearing of 070∘. From B the aeroplane flies to airport C, 60 km from B. Airport C is 90 km from A. Find the two possible directions for the course set by the aeroplane on the second stage of its journey.

I found the ange ABC which is 78.6 but I have no idea on what to do next. The answers are 171.4 and 328.6. Pls help me out :(

Answer 1

Please see below.

Explanation:

.

You calculated the measure of `/_ABC_1` as `78.6^@` which is correct.

The first possible direction for the second stage of the flight would be from Airport `B` to Airport `C_1`.

The vertical line `DE` is showing North to South. Angle `/_ABE=70^@` because it is equal to the original bearing angle from Airport `A`, by virtue of being an alternate interior angle with it.

The small angle `/_EBC_1=78.6^@-70^@=8.6^@`.

The bearing of the direction from `B` to `C_1` is shown by a round arrow starting from near `D` and ending at the line `BC_1` which is the measure of angle `/_DBC_1`. This measure is:

`/_DBC_1=180^@-8.6^@=171.4^@`

The second possible direction for the second stage of the flight would have been from Airport `B` to Airport `C_2`.

Angle `/_ABC_2=78.6^@` as well.

The bearing for this direction from `B` to `C_2` is shown by a round arrow starting again on line `DE` near `D` and ending on line `BC_2`.

The measure of it is:

`360^@-/_DBC_2`

`/_DBC_2=180^@-(70^@+78.6^@)=180^@-148.6^@=31.4^@`

Therefore,

The bearing to `C_2=360^@-31.4^@=328.6^@`