The upper three fourths of a
ship's mast subtend at a
point on the deck, an angle
whose tangent is 0.75. If the
whole mast subtends an
angle º at the same point,
then tan 0 is equal to
Answers
Given : The upper three fourths of a ship's mast subtend at a point on the deck, an angle whose tangent is 0.75.
To find : whole mast subtends an angle θ º and find θ
Solution:
θ = α + β
α = angle subtended by upper three fourths of a ship's mast
β = angle subtended by Lower one fourth of a ship's mast
h = height of mast
x = horizontal Distance
Tan β = (h/4)/x = h/4x
Tanα = 0.75 = 3/4
Tanθ = h/x
Tanθ = Tan(α + β)
=> h/x = (Tanα + Tan β)/( 1- TanαTan β)
=> h/x = ( 3/4 + h/4x) /( 1 - (h/4x)(3/4))
=> h/x = ( 12x + 4h) / ( 16x - 3h)
=> 16hx - 3h² = 12x² + 4hx
=> 3h² + 12x² - 12hx = 0
=> 3h² - 6hx - 6hx + 12x² = 0
=> 3h(h - 2x) - 6x(h - 2x) =0
=> (3h - 6x)(h - 2x) = 0
=> h = 2x
=> h/x = 2
Tanθ = h/x = 2
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