at a certain time of day a 5 foot 11 inch woman casts a 3 foot 11 inch shadow. how tall is a nearby tree that casts a 14 foot 5 inch shadow at the same time of day?
5 feet, 11 inches = 71 inches
3 feet, 11 inches = 47 inches
14 feet, 5 inches = 173 inches
71/47 = x/173
Cross multiply and solve for x.
47x = 12,283
x = 261.34 inches = 21 feet, 9 inches
do this as similar triangles.
(3 11/12)/(5 11/12) = L/(14 5/12)
solve for L . It is probably easier to change to inches...
47/71=LinInches/173
solve for L, then convert back to feet inches. Go Metric, for the life of me, I cannot understand why we are still using feet, yards, inches.
To determine the height of the tree, we can use a proportion based on the information given.
Let's convert the measurements to a consistent unit, such as inches.
The woman's height is 5 feet 11 inches, which converts to 71 inches. Her shadow length is 3 feet 11 inches, which converts to 47 inches.
We can set up a proportion:
Height of woman / Length of woman's shadow = Height of tree / Length of tree's shadow
Substituting the given values:
71 inches / 47 inches = Height of tree / 173 inches (14 feet 5 inches = 173 inches)
To find the height of the tree, we can cross-multiply and solve for the unknown value:
71 inches * 173 inches = 47 inches * Height of tree
12,263 square inches = 47 inches * Height of tree
Now, isolate the Height of the tree by dividing both sides of the equation by 47 inches:
Height of tree = 12,263 square inches / 47 inches
Calculating this, we get:
Height of tree ≈ 260.89 inches
Converting this back to feet and inches, we have:
Height of tree ≈ 21 feet 8.89 inches
Therefore, the nearby tree is approximately 21 feet 8.89 inches tall.