Asked by Ruth
The shadow of a tower standing on a level ground is found to be 2x meters longer when sun's altitude is 30 degree than when it was 45 degree.Find the height of the tower.
Answers
Answered by
Steve
If the tower is h high and the shadow is s long at angle θ, we have
h/s = tanθ, or
s = h/tanθ
So, now we know that
h/tan30 = h/tan45 + 2x
h√3 = h + 2x
h(√3-1) = 2x
h = 2x/(√3-1)
h/s = tanθ, or
s = h/tanθ
So, now we know that
h/tan30 = h/tan45 + 2x
h√3 = h + 2x
h(√3-1) = 2x
h = 2x/(√3-1)
Answered by
Reiny
using only the information you gave, sketch two triangles
let the height of the tower be h
let the length of the shadow at 45° be m
then the length of the shadow at 30° is m+2x
tan 45 = h/m and tan 30 = h/(m+2x)
1 = h/m and 1/√3 = h/(m+2x)
m = h and m+2x = h√3
put 1st into 2nd
h + 2x = h√3
h√3 - h = 2x
h(√3-1) = 2x
h = 2x/√3 - 1)
let the height of the tower be h
let the length of the shadow at 45° be m
then the length of the shadow at 30° is m+2x
tan 45 = h/m and tan 30 = h/(m+2x)
1 = h/m and 1/√3 = h/(m+2x)
m = h and m+2x = h√3
put 1st into 2nd
h + 2x = h√3
h√3 - h = 2x
h(√3-1) = 2x
h = 2x/√3 - 1)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.