Jay is 120 meters from the base of a building and Mary is 40 meters from the base of the building. Jay's angle of elevation when looking at the top of the building is X and Mary's is 2X. What is the height of the building?
What is the height of the building?
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tangent=opposite/adjacent, H=height of building
find the square root of 1/3
square root of 1/3=0.57735
tan of what angle is 0.57735 from the table of tangents ?
the angle x=30 degrees
Use the definition of tangent (opposite/adjacent):
From Jay's point of view, tan (X) = h/120
From Mary's point of view, tan (2X) = h/40
Divide the two equations:
tan(2X)/tan(X) = (h/40)/(h/120) = 3
tan(2X) = 3 tan(X)
Use the double-angle formula
tan(2X) = 2 tan(X) /(1 - tan²(X) )
2 tan(X) /(1 - tan²(X) ) = 3 tan(X)
2 = 3 (1 - tan²(X) )
tan²(X) = 1/3
h=120 tan (30°) ≈ 69 meters
is the height.