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tombfan91
22-09-11, 16:32
A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angel of depression to two consecutive mileposts on the road on the same side of the balloon. The angel of depression are found to be 20 degrees and 23 degrees.

How high is the balloon: please give the answer to one decimal place

Hope you guys can help me out ^_^

the ancient
22-09-11, 16:38
Oh god maths...

Euhm, don't you have to use the cosine, sine or tangent to find out the the height?
I would love to help you but can't you post a little illustration or something?
It would help me to understand it better. :o

toxicraider
22-09-11, 16:42
Draw out everything then use sine rule.
I got 2.55 miles high. Ima show the working in a sec.


Sorry for the dodgy diagram; my camera died on me.
http://img685.imageshack.us/img685/8228/mathsb.png (http://imageshack.us/photo/my-images/685/mathsb.png/)(a=6.535 forgot to write that in)
If I interpreted the question correctly..

Catapharact
22-09-11, 17:29
Draw out everything then use sine rule.
I got 2.55 miles high. Ima show the working in a sec.

But even though the problem says that they are mile posts, we don't know if the balloon is actually a mile away from them. All we know is that the observers saw two mile posts from the balloon and calculated the angle of depression from them.

I don't have time to solve the entire equation for you but I did finish most of it. The rest just requires understanding of simple Algebra.

Here is how I see it:

http://img849.imageshack.us/img849/1344/trig.jpg

Sgt BOMBULOUS
22-09-11, 19:13
I agree with Mr. Toxic.

http://i53.************/bfneic.jpg

Your_Envy*
22-09-11, 19:29
Looking at this gives me such a headache. :p I am so glad I don't have Math and Physics anymore.

klona
22-09-11, 20:00
Looking at all these pictures with numbers and triangles is even more powerful than Titak's Custom Levels' Details! :eek:

tomekkobialka
22-09-11, 20:35
I've checked and I'm sure that the above are the right answers. :tmb:

Now for step two: prove the quadratic equation :vlol:

CerebralAssassin
22-09-11, 20:39
the law of sines always comes in handy doesn't it?:p

tombfan91
23-09-11, 03:00
But even though the problem says that they are mile posts, we don't know if the balloon is actually a mile away from them. All we know is that the observers saw two mile posts from the balloon and calculated the angle of depression from them.

I don't have time to solve the entire equation for you but I did finish most of it. The rest just requires understanding of simple Algebra.

Here is how I see it:

http://img849.imageshack.us/img849/1344/trig.jpg

I got how you got to the plug in the R part. But I then lost you on how you got x by itself. Because I can't seem to do that without cancelling all the x's all together

toxicraider
23-09-11, 10:48
http://img217.imageshack.us/img217/9428/trig.png (http://imageshack.us/photo/my-images/217/trig.png/)

tombfan91
23-09-11, 10:51
^
ahh thank you. I not got the problem. Thank you everyone for your help. I just suck with application problems in general :(