Problema Solution
From a point A on a line from the base of the Washington Monumentˏ
the angle of elevation to the top of the monument is 42.0 degrees.
From a point 100 feet away and on the same lineˏ
the angle to the top is 37.8 degrees.
Find the approximate height of the Washington Monument.
Answer provided by our tutors
make good drawing and use the trigonometry functions
let
x = the distance from point A to the monument
x + 100 = the distance from point 100 ft away on the same line
h = the height of the monument
x = h/(tan (42))
x + 100 = h/(tan (37.8))
plug x = h/(tan (42)) into the last equation
h/(tan (42)) + 100 = h/(tan (37.8))
h*(1/tan(37.8) - 1/tan(42)) = 100
by solving we find
h = 559.97 ft
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the approximate height of the Washington Monument is 559.97 feet.