The Statue of Liberty is approximatly 91.5 meters tall from the base of the pedestal to the tip of the torch. If a theodolite were placed 100 meters from the base of the pedestal, about how far would the theodolite be from the top of the torch?
Sounds like you have a right triangle. The base and height are given; all you need is the hypotenuse.
Yes, you are correct. We have a right triangle where the height of the Statue of Liberty is one side, the distance from the theodolite to the base of the pedestal is another side, and we need to find the length of the hypotenuse, which represents the distance from the theodolite to the top of the torch.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the height of the Statue of Liberty as h, the distance from the theodolite to the base of the pedestal as b, and the distance from the theodolite to the top of the torch as x.
According to the Pythagorean theorem, we have the equation:
x^2 = h^2 + b^2
Plugging in the given measurements:
x^2 = (91.5)^2 + (100)^2
Now we can solve for x by taking the square root of both sides of the equation:
x = √[(91.5)^2 + (100)^2]
Calculating the value on the right side of the equation gives us:
x ≈ 144.43 meters
Therefore, the theodolite would be approximately 144.43 meters from the top of the torch.