A vertical pole A casts a shadow of 44 ft. while a vertical pole B casts a shadow of 85 ft. Pole B is 26 ft taller than Pole A. Find the height of each pole and the angle of elevation of the sun.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A vertical pole A casts a shadow of 44 ft. while a vertical pole B casts a shadow of 85 ft. Pole B is 26 ft taller than Pole A. Let the height of pole A be h, pole b is h + 26 ft tall.

The ratio of the height of each pole to the length of its shadow is the same. This gives:

`h/44 = (h + 26)/85`

=> 85h = 44h + 1144

=> 41h = 1144

=> h = `1144/41`

=> h = 27.9 ft.

The angle of elevation of the sun is `tan^-1((1144/41)/44)` = 32.38 degrees.

The height of pole A is 27.9 ft and pole B is 53.9 ft and the angle of elevation of the sun is 32.38 degrees.

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