SOLUTION: From a certain point, the angle of elevation to the top of a barn is 10 degree .At a point 100 m closer to the barn, the angle of elevation is 50 degree. Label the diagram and calc
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-> SOLUTION: From a certain point, the angle of elevation to the top of a barn is 10 degree .At a point 100 m closer to the barn, the angle of elevation is 50 degree. Label the diagram and calc
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Question 1173354: From a certain point, the angle of elevation to the top of a barn is 10 degree .At a point 100 m closer to the barn, the angle of elevation is 50 degree. Label the diagram and calculate the height of the barn Answer by Theo(13342) (Show Source):
A is the top of the barn.
D is the bottom of the barn.
B is the point with an angle of elevation of 10 degrees to the top of the barn.
C is the point with an angle of elevation of 50 degrees to the to of the barn.
DC has a length of x.
CB has a length of 100.
DB has a length of x + 100.
tangent to angle C is equal to AD / DC = h / x
tangent to angle B is equal to AD / DB = h / (x + 100)
solve for h in both equations to get:
h = x * tan(C) = x * tan(50)
h = (x + 100) * tan(B) = (x + 100) * tan(10)
since they both are equal to h, then they are both equal to each other.
you get:
x * tan(50) = (x + 100) * tan(10)
simplify to get:
x * tan(50) = x * tan(10) + 100 * tan(10)
subtract x * tan(10) from both sides of the equation to get:
x * tan(50) - x * tan(10) = 100 * tan(10)
factor out the x to get:
x * (tan(50) - tan(10)) = 100 * tan(10)
divide both sides of the equation by (tan(50) - tan(10)) to get:
x = 100 * tan(10) / (tan(50) - tan(10))
tan(50) = 1.191753593
tan(10) = .1763269807
solve for x to get:
x = 17.36481777
to confirm, go back to the equation for h.
the equations are:
h = x * tan(C) = x * tan(50)
h = (x + 100) * tan(B) = (x + 100) * tan(10)
replace x with 17.36481777 and tan(B) with .1763269807 and tan(C) with 1.191753593 and solve for h to get:
h = x * tan(C) = x * tan(50) becomes h = 17.36481777 * 1.191753593 = 20.69458396.
