The height of the statue of liberty, where Sarah is making angle of elevation of 61 degrees is 305.5 ft.
The angle of elevation is the angle made between the straight line and the line of observer seeing the object, which is above that straight line.
Here, it is given that the Sarah sights the top of the statue of liberty at an angle of elevation of 61.
Sarah is 5.5 feet tall and is standing 166 feet from the base of the statue. The image is attached below for the given problem.
Here, in the attached image below, the right angle triangle is formed. The tangent angle of the right angle triangle is the ratio of opposite side to the adjacent side. Thus, tangent angle can be given as,
[tex]\tan (60^o)=\dfrac{h}{166}\\h=166\times\tan (60^o)\\h=299.50\rm ft[/tex]
As, The height of the Sarah is 5.5 feet and the height of the statue from the head of the Sarah to the top of it is 299.50 feet. Thus the height of the statue is,
[tex]h_s=5.5+299.50\\h_s=305.5\rm ft[/tex]
Thus, the height of the statue of liberty, where Sarah is making angle of elevation of 61 degrees is 305.5 ft.
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