At a certain time of the day, a 5 foot 1 inch woman casts a 3 foot 4 inch shadow. How tall is a nearby tree that casts a 12 foot 10 inch shadow at the same time of day?

Answer in feet and inches.  Do not round until the final answer. Then round to the nearest whole inch as necessary.

since the ratio of height:shadow is constant,

5'1"/3'4" = h/12'10"

That's kind of messy, so convert all the values to just inches. Find h, then convert it back to feet&inches.

To find the height of the nearby tree, we can set up a proportion using the given information. Let's assume the height of the tree is x feet and y inches.

The proportion would be:

(Height of the woman)/(Length of her shadow) = (Height of the tree)/(Length of its shadow)

Now let's convert the heights and lengths to inches for easier calculations.

The height of the woman is (5 feet * 12 inches) + 1 inch = 61 inches.

The length of her shadow is (3 feet * 12 inches) + 4 inches = 40 inches.

Substituting the values into the proportion, we have:

61 inches / 40 inches = (x feet * 12 inches + y inches) / (12 feet * 12 inches + 10 inches)

Simplifying the equation:

61 / 40 = (12x + y) / (144 + 10)

Now, cross-multiply to find (12x + y):

61 * 154 = 40 * (12x + y)

9394 = 480x + 40y

To find the height of the tree, we need to know either the value of x or y. Let's assume y = 0 (no remaining inches after converting to feet).

9394 = 480x + 40 * 0

9394 = 480x

x = 9394 / 480 = 19.5292 feet

Now, round the height of the tree to the nearest whole inch:

19 feet = 19 * 12 inches = 228 inches

So, the nearest whole inch for the height of the tree is 228 inches.