The Statue of Liberty is about 151 feet tall. If the angle of elevation from a tree in Liberty State Park to the statue's top is 1.5 degrees, how far is the tree from the statue?
cot 1.5 DEGREES= h/ 151
151 cot 1.5= h
h= ________
1.51
cot 1.5 degrees = h/151
151 cot 1.5 degrees = h
h = _______________
To find the distance from the tree to the Statue of Liberty, we can use trigonometry. We know the height of the statue is 151 feet and the angle of elevation from the tree to the top of the statue is 1.5 degrees.
Using the tangent function, we can set up the equation:
tan(1.5 degrees) = height of the statue / distance from the tree to the statue
tan(1.5 degrees) = 151 feet / distance from the tree to the statue
Now, to isolate the distance, we can rearrange the equation:
distance from the tree to the statue = 151 feet / tan(1.5 degrees)
Using a scientific or graphing calculator, we can find the tangent of 1.5 degrees, which is approximately 0.02618.
Plugging this value into the equation, we get:
distance from the tree to the statue = 151 feet / 0.02618
Simplifying this expression, we find:
distance from the tree to the statue ≈ 5,772.2 feet
Therefore, the tree is approximately 5,772.2 feet away from the Statue of Liberty.