At a certain time of day, a 5 foot 10 inch woman cast a 3 foot 3 inch shadow. How tall is a nearby tree that casts a 13 foot 8 inch shadow at the same time of day
Cross multiply and solve for x. Then change your answer to feet and inches.
70/39 = x/164
To solve this problem, we can set up a proportion between the heights of the woman and the tree relative to their respective shadows.
First, let's convert the measurements to inches for consistency.
The woman's height is 5 feet 10 inches, which is equivalent to (5 x 12) + 10 = 70 inches.
Her shadow's length is 3 feet 3 inches, or (3 x 12) + 3 = 39 inches.
The tree's shadow's length is 13 feet 8 inches, which is (13 x 12) + 8 = 152 inches.
Now, we can set up the proportion:
Woman's height / Woman's shadow = Tree's height / Tree's shadow
Plugging in the known values:
70 inches / 39 inches = Tree's height / 152 inches
To find the height of the tree, we can cross-multiply and then divide:
70 inches * 152 inches = 39 inches * Tree's height
10,640 inches = 39 inches * Tree's height
Now, we can solve for the height of the tree:
Tree's height = 10,640 inches / 39 inches
Tree's height ≈ 272.82 inches
Therefore, the nearby tree is approximately 272.82 inches tall.