The Whooping Crane Is Canada's Tallest Bird. When The Angle Of Elevation Of The Sun Decreases From 30º To 25º, The Length Of A Whooping Crane's Shadow Increases By 62cm....

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We know that the angle of the triangle opposite to the base is say theta is the same as 90 - the angle of elevation of the sun. This is the angle opposite to the base which is the length of the shadow
Assuming h is the hypotenuse we know
since sin(theta) = length of shadow / hyp
so at 30 deg theta = 60 degrees, lets say the length is x
so at 25 deg theta = 65  the length of shadow becomes x + 62

so for case 1 - sin 60 = x / hyp
and for case 2 : Sin 65 = x+62 / hyp

getting values of sin60 and sin 65 we get
0.8660x hyp = x and
0.906 x hyp = x + 62.
so hyp = 0.906x + 56.19
substitute this in the other equation, we get
0.8660(0.906x + 56.19) = x
 0.785x + 48.661 = x
so 0.215 x = 56.19
so x = 261.35 cms
and x+62 = 261.35 + 62 = 323.35
But we want to calculate the height
using value of x, we know that
tan theta = x / y where theta = 60
so y = 261.35/tan60 = 261.35/1.732
so y = 150.89 cms = height of the crane

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