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?
Repeat of your previous problem
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To find the distance between the tree and the Statue of Liberty, we can make use of trigonometry. We know the height of the statue and the angle of elevation, so we can set up a right triangle.
In this case, the height of the Statue of Liberty is the opposite side of the angle, and the distance from the tree to the statue is the adjacent side of the angle. We want to find the adjacent side.
We can use the trigonometric function tangent to find the adjacent side:
tan(angle) = opposite/adjacent
Since we want to find the adjacent side, we can rearrange the formula:
adjacent = opposite / tan(angle)
Plugging in the values we know:
opposite = height of the Statue of Liberty = 151 feet
angle = 1.5 degrees
We need to convert the angle from degrees to radians to use it in the tangent function. We know that 180 degrees is equal to π radians:
angle in radians = (angle in degrees) * (Ï€/180)
So, the angle in radians is:
1.5 degrees * (π/180) ≈ 0.0262 radians
Now we can calculate the distance from the tree to the statue:
adjacent = 151 feet / tan(0.0262 radians)
Using a calculator to perform the tangent function:
adjacent ≈ 151 feet / 0.0262 ≈ 5756.11 feet
Therefore, the tree is approximately 5756.11 feet away from the Statue of Liberty.
cot 1.5 degrees= h/151
151 cot 1.5= h
h= _________