Question

The angle of elevation to the top of the Empire State Building in New York is found to be 16 degrees from the ground at a distance of 1091 meters from the base of the building.

Using this information, find the height of the Empire State Building. Round your answer to the nearest hundredth of a meter.

Answer 1

To find the height of the Empire State Building, we can use trigonometry. We have the angle of elevation (16 degrees) and the distance from the base of the building (1091 meters). We can use the tangent function to calculate the height.

The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the building, and the adjacent side is the distance from the base.

So, we can set up the equation: tan(16 degrees) = height / 1091 meters.

Now we can solve for the height by multiplying both sides of the equation by 1091 meters and taking the tangent of 16 degrees.

height = 1091 meters * tan(16 degrees).

Calculating this, the height of the Empire State Building is approximately 305.33 meters.