Some trigonometry in three dimensions. (1 Viewer)

[Carl5]

David walks along a straight road. At one point he notices a tower on a bearing of 053 degrees with an angle of elevation of 21 degrees. After walking 230m, the tower is on a bearing of 342 degrees, with an angle of elevation of 26 degrees. Find the height of the tower correct to the nearest metre.

Also...

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.

I just can't do them...

 

[hscishard]

I hate 3d trig.

I think the 2nd one is 6deg 7'
I used normal right angled triangles to find the hypotenuses. Then since it was only 20 mins (1/3 hr) it travelled 950/3m. Then I used the cosine rule.

I keep getting different answers for the 1st one...wtf

 

[ohexploitable]

For the first one, 56m.

 

[ohexploitable]

For the second one, 11° 10'.

 

[hscishard]

How'd you do it?

 

[ohexploitable]

How'd you do it?

For the first one, find one unknown base length in terms of h, then use sine rule and solve for h.

For the second one, find both unknown base lengths, then use cosine rule to find the required angle.

 

[hscishard]

I did that.
Wait did you use tan anywhere?

For the 2nd one..don't you find the hypotenuses and then use the cosine rule for that?

 

[Carl5]

For the first one, 56m.

Incorrect It's 84

For the second one, 11° 10'.

Correct!

For the second one, find both unknown base lengths, then use cosine rule to find the required angle.

Thank you! Ended up being easier than I thought haha.