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

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