Asked by Dend
Two observers on opposite sides are 350m apart and are looking at a balloon if the angles of elevation from each observer are 30degree and 60degree respectively,how high is the balloon?
Answers
Answered by
Reiny
make your sketch
let the point below the ballon be P
let the distance from the 60° position to P be x
then the other distance is 350-x
You have two right-angled triangles
let the height be h m (the common side to the two triangles)
for the 1st triangle:
tan60 = h/x
h = xtan60
for the 2nd:
tan30 = h/(350-x)
h = (350-x)tan30
so
xtan60 = (350-x)tan30
xtan60 = 350tan30 - xtan30
xtan60 + xtan30 = 350tan30
x(tan60 + tan30) = 350tan30
x = 350tan30/(tan60+tan30)
back to the 1st triangle
h = xtan60
h = 350tan30tan60/(tan60+tan30)
= ...
Only now would I reach for my calculator and do all the calculations in one swoop using the ( ) keys to make sure of my order of operations.
I got appr 151.55 m
let the point below the ballon be P
let the distance from the 60° position to P be x
then the other distance is 350-x
You have two right-angled triangles
let the height be h m (the common side to the two triangles)
for the 1st triangle:
tan60 = h/x
h = xtan60
for the 2nd:
tan30 = h/(350-x)
h = (350-x)tan30
so
xtan60 = (350-x)tan30
xtan60 = 350tan30 - xtan30
xtan60 + xtan30 = 350tan30
x(tan60 + tan30) = 350tan30
x = 350tan30/(tan60+tan30)
back to the 1st triangle
h = xtan60
h = 350tan30tan60/(tan60+tan30)
= ...
Only now would I reach for my calculator and do all the calculations in one swoop using the ( ) keys to make sure of my order of operations.
I got appr 151.55 m
Answered by
dend
thank you sir it is really helpful :)
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