a christmas tree is 34 feet tall. it casts a shadow 24 feet long. toms christmas tree is standing beside the tree at rockefeller center and is 5 feet 8 inches tall. how long of a shadow would toms tree cast?
Let x be the length of the shadow cast by Tom's tree. Set up a ratio:
5ft 8in = 5+(8/12)ft = 17/3ft
24/34 = x/(17/3)
x=?
To find out how long of a shadow Tom's tree would cast, we can set up a proportion using the height and shadow length of the Rockefeller Center Christmas tree.
Let's convert Tom's height to feet. Since there are 12 inches in a foot, 8 inches can be represented as 8/12 or 2/3 feet. Therefore, Tom's height is (5 + 2/3) feet, which is equal to 17/3 feet.
Now, we can set up the proportion:
Height of Rockefeller Center tree / Shadow length of Rockefeller Center tree = Height of Tom's tree / Shadow length of Tom's tree
Substituting the given values:
34 feet / 24 feet = (17/3) feet / Shadow length of Tom's tree
To find the shadow length of Tom's tree, we cross-multiply and solve for it:
Shadow length of Tom's tree = (24 feet * 17/3 feet) / 34 feet
Simplifying this expression:
Shadow length of Tom's tree = (408/3) feet / 34 feet
Shadow length of Tom's tree ≈ 12 feet
Therefore, Tom's Christmas tree would cast a shadow that is approximately 12 feet long.