Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
a tower 7 metres high stands on top of building which is 9 metres high. An observer at the bottom of the building notices that,...Asked by haro
A tower 7 metres high stands on top of building which is 9 metres high. An observer at the bottom of the building notices that, as she walks away from the building, the angle theta which the tower subtends at her eyes seems to increase in size for a certain distance and then to decrease; determine what position of x maximises the angle theta.
Solve problem by using both a trigonometric and a geometric approach.
Solve problem by using both a trigonometric and a geometric approach.
Answers
Answered by
Steve
set up a diagram. You can see that if the angle to the top of the building is a, then
x/9 = cot(a)
x/16 = cot(a+θ)
θ = arctan(x/9) - arctan(x/16)
dθ/dx = 0 when x=12
as shown here:
https://www.wolframalpha.com/input/?i=arctan%28x%2F9%29+-+arctan%28x%2F16%29
x/9 = cot(a)
x/16 = cot(a+θ)
θ = arctan(x/9) - arctan(x/16)
dθ/dx = 0 when x=12
as shown here:
https://www.wolframalpha.com/input/?i=arctan%28x%2F9%29+-+arctan%28x%2F16%29
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.