Problema Solution
A statue 20 feet high stands on top of a base. From a point in front of the statue, the angle of elevation to the top of the statue is 48 degrees, and the angle of elevation to the bottom of the statue is 42 degrees. How tall is the base?
Answer provided by our tutors
let
h = the height of the base
d = the distance of the base to the point of view
(20 + h)/d = tan(48)
h/d = tan(42) follows d = h/(tan(42))
plug d = h/(tan(42)) into (20 + h)/d = tan(48):
(20 + h)/(h/(tan(42)) = tan(48)
by solving we find:
h = 85.67 ft
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the base is 85.67 ft tall.