Math Is Fun Forum

Malgrif

Guest

Trig problem

Arg I can't find my error could someone help me please, i'm going insane...

From two tracking stations A and B, 350km apart, a UFO is sighted at C above AB, making angleCAB = 32°, angleCBA = 54°. Find the height of the UFO.

Here's what i've tried so far... I'm making an error somewhere but I can't find out where...

tan32=x/AD, tan54=x\DB, DB + AD = 350
(CD is the height D is the point that touches the ground)

From there I isolated for variables.

x=ADtan32, x=DBtan54, AD=350 - DB

Sub them into eachother

(350 - DB)tan32=DBtan54

350tan32 - DBtan32= DBtan54

Now isolating DB

350tan32 = DBtan54 + DBtan32

350tan32 = DB(tan54+tan32)

(350tan32)/(tan54 + tan32)=DB

Now to solve for height...(x = height of CD)

x = DBtan54
x = [(350tan32)/(tan54 + tan32)]tan54
x = 138.043885km

Alright now here's my problem when I solve for AD instead and try to find the height that way, I get a differnt height.

AD = 350 - DB
AD = 350 - [(350tan32)/(tan54 + tan32)]

x = ADtan32
x = [350 - [(350tan32)/(tan54 + tan32)]]tan54
something that's not 138km...

Help please!!! if you could solve the problem and point out my math error thanks.

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Trig problem

actually, if you know that DB+AD=350 , you could change it to  AD=x/tan32 , DB=x/tan54
AD+DB = x( 1/tan32+1/tan54)=350 , your work looks fine, I think there might be some minor error

integer

Member

Registered: 2008-02-21

Posts: 79

Re: Trig problem

x = DBtan54
x = [(350tan32)/(tan54 + tan32)]tan54
x = 138.043885km

x = [ (350tan32) / (tan54 + tan32) ]   tan54  = 150.416

My calculator does not yield the 138.04 value.
Check your batteries

Incidental question:
For a really precise answer, what is the elevation of the points A and B?
When you say "above the ground" are you referring to see level, actual ground, or the earth gravity model?  In any case what is the Latitude/Longitude of the observation points? Does Refraction need to be accounted for?   

Just an observation:
point A is approx. 4.5 km above "ground" and point B is approx. 1 km above.

assuming they are earth based.

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Trig problem

x = DBtan54
x = [(350tan32)/(tan54 + tan32)]tan54
x = 138.043885km

x = [ (350tan32) / (tan54 + tan32) ]   tan54  = 150.416

My calculator does not yield the 138.04 value.
Check your batteries

Incidental question:
For a really precise answer, what is the elevation of the points A and B?
When you say "above the ground" are you referring to see level, actual ground, or the earth gravity model?  In any case what is the Latitude/Longitude of the observation points? Does Refraction need to be accounted for?   

Just an observation:
point A is approx. 4.5 km above "ground" and point B is approx. 1 km above.

assuming they are earth based.

Wow, I guess you dont need to consider it as a Spherical triangle, that's a lot of trouble lol