See the last picture at the bottom of this web page (for a pic of this exact problem).
Using ratios,
Tree height = T
15/66 = 6.33/T
15T = 512.73
T = 34.182
T = 34.182 when getting this answer from my question: to estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree's shadow end at the same point. Dave is 6 feet 4 inches tall and his shadow is 15 feet long. If he is standing 66 feet away from the tree, what is the height of this tree? why was it 6.33/T (where did that come from?)
Shannon, I'm very sorry. The set-up is wrong (1st line), but the rest is correct. I have no idea where I got that first line.
http://member.tripod.com/~BDaugherty/GCSEMaths/shapes.html
In the picture, the ratio is
T/30 = 2/3
3T = 60
T = 20
Your problem, with the corrected first line is
Using ratios,
Tree height = T
T/81 = 6.33/15
15T = 512.73
T = 34.182
To estimate the height of the tree, we can use ratios.
First, let's define some variables:
- Tree height: T
- Dave's height: 6 feet 4 inches (which can be converted to feet as 6 + 4/12 = 6.33 feet)
- Dave's shadow length: 15 feet
- Distance between Dave and the tree: 66 feet
Now, we want to set up a ratio using these values. We know that the ratio of Dave's height to his shadow length is the same as the ratio of the tree's height to the length of its shadow.
So, we can set up the following ratio:
(Dave's height)/(Dave's shadow length) = (Tree's height)/(Length of tree's shadow)
Plugging in the given values:
(6.33)/(15) = (T)/(Length of tree's shadow)
Simplifying:
6.33/15 = T/(Length of tree's shadow)
Now, we know that Dave's shadow and the tree's shadow end at the same point, so their lengths are the same. Therefore, we can replace "Length of tree's shadow" with 15.
So, we have:
6.33/15 = T/15
To solve for T, we can cross-multiply and solve the resulting equation:
(6.33 * 15) = T * 15
After multiplying:
94.95 = 15T
Now, to find T, we can divide both sides of the equation by 15:
94.95/15 = T
After dividing:
6.33 = T
Therefore, the height of the tree is approximately 6.33 feet.
The value of 6.33/T in the initial setup of the ratio came from dividing Dave's height (6.33 feet) by his shadow length (15 feet) to find the ratio of his height to his shadow length. We then set up the same ratio with the tree's height (T) and the length of the tree's shadow, which was also 15 feet since Dave and the tree cast shadows that ended at the same point.