To get the best view of the statue of liberty, you should be at the position where angle theta is a maximum? - distance from statue of liberty to niagra falls
When the statue is 92 meters high, including the base, should be 46 meters away from the base? Tip: Find a formula for the angle theta by their distance from the base. Use this function to optimize theta, indicating that theta is greater than or equal to 0 and less than or equal to PI / 2
Distance From Statue Of Liberty To Niagra Falls To Get The Best View Of The Statue Of Liberty, You Should Be At The Position Where Angle Theta Is A Maximum?
2 comments:
There is no limitation to your problem. If your boundaries are
- Theta must be less than or equal to PI / 2
- You want to maximize Theta
then theta = pi / 2
How far would you be? 0 meters.
Construct a triangle ABC, such as:
The angle A is the base of the pedestal;
The vertical part of AB represents the statue (with feet), length 92, B is the dot represents the head of the statue.
The base of the triangle represents the distance between you (point C) and the foot of the pedestal.
Place the letter D, the center of the line AB (the beginning of the base). Now the segment CD (from your computer takes off) to the top of the pedestal. Want to maximize the angle \\ \\ \\ \\ \\ \\ \\ \\ u0026lt, BCD, adopted some of their field of vision by a statue without a pedestal.
Looking for X = the length of the base, ie the length of the segment AC. The angle you try to optimize it ...
\\ \\ \\ \\ \\ \\ \\ \\ U0026lt; BCD = \\ \\ \\ \\ \\ \\ \\ \\ u0026lt; BCA - \\ \\ \\ \\ \\ \\ \\ \\ u0026lt; DCA
Arccotg = (x/92) - arccotg (X/46).
Determine which of d (arccotg (x)) / dx = -1 / (1 + x ^ 2):
\\ \\ \\ \\ \\ \\ \\ \\ U0026lt; BCD '(x) = -1 / [92 (1 + x ^ 2 / 92 ^ 2)] + 1 / [46 (1 + x ^ 2 / 46 ^ 2)]
After a little algebra, we find that it is equal to zero when x = sqrt (92 * 46) = 46sqrt (2) = approximately 65 years. The resulting corner arccotg (sqrt (1 / 2)) - ARccotg (sqrt (2)) = 54.74 ° - 35.26 ° = 19.47 °.
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