Calculating the Height of Statue of Liberty
In the image, you're provided with a right triangle where the length of the hypotenuse is 340 feet and the length of the base is 150 feet. You need to find the height of the Statue of Liberty, which corresponds to the vertical side of the triangle.
To solve for the height, you can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
The theorem is expressed as: a² + b² = c²
Here, we are looking for the length of a (the height), while we know the lengths of b (the base, 150 feet) and c (the hypotenuse, 340 feet).
We can rearrange the theorem to solve for a:
a² = c² - b²
Plug in the given lengths:
a² = (340)² - (150)²
a² = 115,600 - 22,500
a² = 93,100
Now, take the square root of both sides to find the value of a:
a = √93,100
a ≈ 305 feet
So, the height of the Statue of Liberty is approximately 305 feet to the nearest foot.
