SOLUTION: I need help with this word problem please. Felita decided to take a ride in a hot air balooon.as the air ballon rises vertically the angle of elevation from a point P on the gro

Question 756463: I need help with this word problem please.
Felita decided to take a ride in a hot air balooon.as the air ballon rises vertically the angle of elevation from a point P on the ground level 120 km from the point Q directly underneath the balloon changes from 19 degree 20 seconds to 31 degrees 50 seconds.Approximatly how far does the ballon rise during this period?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
NOTE # 1:
A hot air balloon cannot get that high and would be hard to see from 120 km away. A helium balloon can rise higher than a hot air balloon, and Felix Baumgartner supposedly got to 39km on a helim balloon for his skydiving record. (He was wearing some sort of spacesuit, because there is very little air pressure at that altitude). The problem would be more believable if the distance PQ was 12.0 km instead of 120 km. However, I'll calculate based on PQ=120km.

The ballon rises from point R to point S, both directly above point Q.
angle QPR = 19 degree 20 seconds
angle QPS = 31 degrees 50 seconds
QR = PQtan(QPR)
QS = PQtan(QPS) and
balloon rise = QS - QP = PQtan(QPS) - PQtan(QPR) = PQ(tan(QPS) - tan(QPR))
Using approximate values for those tangents,
QR = PQtan(QPR) = 120km X 0.344436 = 41.33232km
QS = PQtan(QPS) = 120km X 0.601191 = 72.14292km, and
balloon rise = 120km (0.601191 - 0.344436) = 120km X 0.256755 = 30.8106km

NOTE:
If the calculator cannot handle minute and second fractions of a degree, you will have to convert to degrees.
There are 60 minutes in 1 degree and 60 seconds in one minute, so there are
seconds in 1 degree.
19 degree 20 seconds = =19.00555555....
31 degree 50 seconds = =31.01388888888....
RELATED QUESTIONS
Hello, my name is niya. I am in the eighth grade and taking algebra honors. I need help... (answered by Edwin McCravy,josmiceli)

hi,i know this is not a Math question but i need help ver very bad. I understand the... (answered by solver91311)

A hot air balloon can lift 2 tones the basket weights 800kg it has 15 sandbags to keep... (answered by ikleyn)

how long would it take a hot air ballon to go from new york to houston at 3mph. if a... (answered by josmiceli)

Hello math tutor, i need help on this word problem. i need to use this formula : {{{... (answered by Alan3354)

Joel wants to determine the height of a hot air balloon that is sitting on the ground.... (answered by stanbon)

Please help me solve this word problem: Jerry takes 6 hours to ride a bicycle 30... (answered by lwsshak3)

when a spherrical ballon is filled with air, it has a diameter of 6 inches which of... (answered by Boreal)

I need to solve this by factoring but can't seem to get it! Suppose the altitude of a... (answered by rapaljer)