Ramsay is standing 2906 ft away from the base of the Empire State building that is 1453 ft tall. What is the angle of elevation when she looks at the top of the building? Round to the nearest hundredth.
A
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B
tan(angle ABC)= 1453/2906
To find the angle of elevation when Ramsay looks at the top of the Empire State building, we can use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.
In this case, Ramsay is standing 2906 ft away from the base of the building, which is the adjacent side, and the height of the building is the opposite side.
Let's call the angle of elevation "x". Using the tangent function, we can set up the following equation:
tan(x) = opposite ÷ adjacent
tan(x) = 1453 ÷ 2906
Now, we can calculate the value of x by taking the inverse tangent (arctan) of both sides of the equation:
x = arctan(1453 ÷ 2906)
Using a calculator, we find that x ≈ 28.50 degrees.
Therefore, the angle of elevation when Ramsay looks at the top of the Empire State building is approximately 28.50 degrees.