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geometry

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A tower casts a shadow of 64 feet. A 6-foot tall pole near the tower casta a shadow 8 feet long. How tall is the tower.

  • geometry - ,

    The height-to-shadow-length ratio is the same for both pole and tower. That is because the sun is at the same angle in the sky for both. You have similar right triangles formed by object, its shadow on the ground and the slated sunbeam that comes down to the ground from the top.

    Let H be the tower height.

    H/64 = 6/8 = 3/4

    H = 64*3/4 = 48 feet

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