3D Trig Help 1 (1 Viewer)

[Andy005]

A hot air balloon flying at 950m/h at a constant altitude of 3000m is observed to have an angle of elevation of 78 degrees. After 20 minutes, the angle of elevation is 73 degrees. Calculate the angle through which the observer has turned during those 20 minutes.

Working Out: https://drive.google.com/open?id=0B_RlXPQTW1cRenJRUWc3NmdIUUU

Answer is 11˚10'

What am I doing wrong?

Thanks for the help.

PS: Sorry for image quality.

 

[SirKeynes]

Re: 3D Trig Help

To find Ø in the cosine formula You are using the diagonals x and y.

You should instead use the base sides, which can be found with tan ratios.

I.e swap sin for tan

 

[He-Mann]

Re: 3D Trig Help

It depends on where exactly the observer is looking at.

If the line of sight of the observer is parallel to the (flat) ground and directly towards the y-axis of the balloon, then SirKeynes' answer is right.

Otherwise, if the line of sight of the observer is directly towards the center of the balloon, then Andy005's answer is right.

 

[SirKeynes]

Re: 3D Trig Help

Yes the question could definetely be clearer! (For instance you can also interpret the plane to travel in his current line of sight) But by "turning" this is how I interpreted it.