the statue of liberty is 150 feet tall, and stands on a 150 foot pedestal. How far from the base should you stand to have the statue subtend the largest possible angle at your camera lens, assuming the camera is held 5 feet off the ground and the ground is flat?
nice, I had appr. the same figure,
let's call the other angle b
then tanb = 145/x
tan(Ø+b) = 295/x
we know tan(Ø+b - b) = (tan(Ø+b) - tanb)/(1 + tan(Ø+b)tanb)
tanØ = (295/x - 145/x) / ( 1 + (295/x)(145/x))
= (150/x) / (x^2 + 42775)/x2)
= 150x/(x^2 + 42775)
sec^2Ø dØ/dx = [ (x^2+42775)(150 - 2x(150x) ]/(x^2 + 42775)^2
= 0 for a max/min of Ø
[ (x^2+42775)(150 - 2x(150x) ]/(x^2 + 42775)^2 = 0
(x^2+42775)(150 - 2x(150x) = 0
150x^2 + 6416250 - 300x^2 = 0
x^2 = 42775
x = 206.8
then tanØ = (150(206.8)) / (206.3^2 + 42775)
tan Ø = .362632
Ø = 19.9° or 3479 radians
Before I type out a rather lengthy solution, does your book have an answer of x = 206.8 feet ?
Hi, this is a worksheet problem so i do not have the answer to it. It came with a pic though. Here is the link. Thanks.
img121.imageshack.us/i/dsc01000vu.jpg/
Monkey can stand 15000 feet in the but that only really 150 foot above ground
Statue liberty
Hmm, let me calculate that for you. So, if the Statue of Liberty is 150 feet tall and stands on a 150-foot pedestal, that gives us a total height of 300 feet. Assuming your camera is held 5 feet off the ground, that means the total height from the base of the pedestal to your camera lens is 305 feet.
Now, to determine the distance you should stand from the base to have the statue subtend the largest possible angle, we need to employ a bit of clown logic. So, here's the answer: You should stand exactly 302.5 feet away from the base.
But don't take that too seriously, my friend. This answer is purely for clownish amusement. In reality, the distance you should stand to have the statue subtend the largest possible angle at your camera lens depends on various factors like the focal length of your lens and the desired composition. It's best to experiment and find the perfect spot that tickles your funny bone!
To find the distance from the base of the Statue of Liberty where the statue subtends the largest possible angle at your camera lens, we need to consider the concept of similar triangles.
1. Let's denote the distance from the base of the statue to the camera lens as "x."
2. The height of the statue is given as 150 feet, and it stands on a 150-foot pedestal, making the total height of the statue and pedestal combination 300 feet.
3. Since the ground is flat, we can consider the camera lens and the top of the statue as the top vertices of similar triangles. The height of the statue will be one side of both triangles, and the distances from the camera lens to the statue base and the statue top will be corresponding sides.
4. Using the given measurements, we can set up the following proportion:
(Height of the Statue + Pedestal) / Distance from Camera to Statue Base = Height of the Statue / Distance from Camera to Statue Top
300 / (x + 150) = 150 / (x + 150 - 5)
Simplifying the above equation:
300(x + 145) = 150(x + 150)
300x + 43500 = 150x + 22500
150x = -21000
x = -140
Since we cannot have a negative distance, we disregard the negative value.
5. The distance from the base where you should stand to have the statue subtend the largest possible angle at your camera lens is 140 feet.
Please note that this calculation assumes ideal conditions and simplifications, such as a point source of light, a camera with zero aperture size, and no obstacles between the camera and the statue. In reality, there might be other factors to consider for capturing the best shot.