Homework Help: math

Posted by Chris on Sunday, May 2, 2010 at 11:33pm.

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?

math - Reiny, Monday, May 3, 2010 at 1:01am
Before I type out a rather lengthy solution, does your book have an answer of x = 206.8 feet ?
math - Daniel, Monday, May 3, 2010 at 1:33am
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/
math - Reiny, Monday, May 3, 2010 at 8:19am
nice, I had appr. the same figure,
let's call the other angle b

then tanb = 145/x
tan(Ų+b) = 295/x

we know tan(Ų+b - b) = (tan(Ų+b) - tanb)/(1 + tan(Ų+b)tanb)
tanŲ = (295/x - 145/x) / ( 1 + (295/x)(145/x))
= (150/x) / (x^2 + 42775)/x2)
= 150x/(x^2 + 42775)

sec^2Ų dŲ/dx = [ (x^2+42775)(150 - 2x(150x) ]/(x^2 + 42775)^2
= 0 for a max/min of Ų

[ (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 tanŲ = (150(206.8)) / (206.3^2 + 42775)
tan Ų = .362632
Ų = 19.9° or 3479 radians

Answer this Question

Related Questions

geometry - A 5-foot tall girl stands 15 feet from a statue. She must look at an ...
Math(plase help me solve) - The Statue of Liberty is approximatly 91.5 meters ...
Trigonometry - The Statue of Liberty is approximatly 91.5 meters tall from the ...
Trigonometry - If someone could tell me if this is correct, it would really help...
Precalculus - 1. A man stands 12 feet from a statue. The angle of elevation from...
math - There are two 100-foot poles. A 150-foot rope connects them at the top. ...
math - you are standing 15 feet from a statue the angle of the elevation from ...
Algerbra - I need help solving the b portion of the equation. 15. Assume that a ...
algebra1 - A)a plane flies at the height of 1800 feet directly over 150-foot-...
CHEMISTRY PLEASE HELP - For the reaction A + 2B + C ----> 2 D + E the ...

For Further Reading

First Name:
School Subject:
Answer: