mary is 5ft 9 inches tall. she casts a 2 ft shadow. the tree casts a 7 foot shadow. how tall is the tree?
9 inches * (1 foot / 12 inches )
= .75 foot
so
5.75 / 2 = h/7
multiply both sides by 14
5.75 * 7 = 2 h
h = 7.75 * 7/2
h = 27.125
which is 27 1/8 feet
which is 27 feet 1 and 1/2 inches :)
To determine the height of the tree, we can use the concept of similar triangles.
First, we need to find the ratio of Mary's height to her shadow and the ratio of the tree's height to its shadow.
Mary's height: Mary's shadow = 5 ft 9 in : 2 ft
Tree's height: Tree's shadow = ? : 7 ft
Since the ratios of corresponding sides of similar triangles are equal, we can set up the following proportion:
(Height of Mary) / (Length of Mary's shadow) = (Height of the Tree) / (Length of the Tree's shadow)
Substituting the given values:
(5 ft 9 in) / (2 ft) = (Height of the Tree) / (7 ft)
To simplify the calculation, let's convert Mary's height to feet and inches into inches. 5 ft 9 in is equivalent to 69 inches.
(69 in) / (2 ft) = (Height of the Tree) / (7 ft)
Now, we can cross-multiply and solve for the height of the tree:
69 inches * 7 ft = 2 ft * (Height of the Tree)
483 inches = 2 ft * (Height of the Tree)
Divide both sides by 2 ft:
(483 inches) / (2 ft) = Height of the Tree
Now, let's convert the height of the tree back to feet and inches:
(483 inches) / (12 inches/ft) = (Height of the Tree) ft
Thus, the height of the tree is 40 ft and 3 in.