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The Statue of Liberty stands on a 150 ft pedestal. From a point 280 ft from the base of the pedestal, the angle of elevation to the top of the torch is 47 degrees. Find the height of the statue.

Answer :

The height of the Statue of Liberty is approximately 152.776 feet (or 153 feet rounded).

To find the height of the Statue of Liberty, we can use trigonometry and set up a right triangle. Let's denote the height of the statue as "h."

The statue stands on a 150 ft pedestal, so the total height from the base to the top of the torch is h + 150 ft. From a point 280 ft from the base of the pedestal, we can consider this distance as the base of our triangle.

Now, let's consider the angle of elevation. The angle of elevation is the angle formed between the horizontal line from the observer's eye to the base of the pedestal and the line of sight from the observer's eye to the top of the torch. In this case, the angle of elevation is 47 degrees.

Using trigonometry, we can set up the following relationship:

tan(47°) = (h + 150) / 280

To solve for h, we can rearrange the equation:

h + 150 = 280 * tan(47°)

h = 280 * tan(47°) - 150

Now, let's calculate the value of h:

h ≈ 280 * 1.0724 - 150

h ≈ 302.776 - 150

h ≈ 152.776 ft

Therefore, the height of the Statue of Liberty is approximately 152.776 feet.

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