To determine the height of a pine tree, you measure the shadow cast by the tree and find it to be 20 feet long. Then you measure the shadow cast by a 36-inch tall oak sapling and find it to be
d = 12 inches long. Estimate the height of the pine tree.
since the ratio of height:shadow is the same,
h/20 = 36/12
thanks oobleck
Well, if the shadow of the oak sapling is 12 inches, then we can use some good old-fashioned math to estimate the height of the pine tree. Let's call the height of the pine tree "p".
If the shadow of the pine tree is 20 feet (240 inches), then we can set up a proportion:
p/240 = 36/12
Cross-multiplying, we get:
12p = 240 * 36
So, the height of the pine tree would be:
p = (240 * 36) / 12
Now, let me just pull out my trusty calculator to do the math...
*clownishly presses calculator buttons*
Okay, give me a moment...
*pretends to struggle with the calculator*
Ah! Here we go!
Drumroll, please...
The estimated height of the pine tree is approximately 720 feet!
Now, that's one tall tree! Just be careful not to get a crick in your neck while looking up at it.
To estimate the height of the pine tree, we can use the concepts of similar triangles.
First, we need to convert the lengths to the same units. Since the height of the oak sapling is given in inches, we'll convert the shadow of the pine tree to inches as well.
Given:
Shadow of the pine tree = 20 feet
Shadow of the oak sapling = 12 inches
Converting the shadow of the pine tree to inches:
1 foot = 12 inches
20 feet = 20 * 12 inches = 240 inches
Now, we can set up a proportion using the similar triangles formed by the tree and its shadow, and the sapling and its shadow.
Let h be the height of the pine tree.
Proportion:
(height of the pine tree) / (shadow of the pine tree) = (height of the oak sapling) / (shadow of the oak sapling)
Plugging in the values:
h / 240 inches = 36 inches / 12 inches
Next, we can solve this proportion to find the estimated height of the pine tree, h.
Cross-multiplying:
12h = 240 * 36
Dividing by 12:
h = (240 * 36) / 12
Calculating:
h = 720 inches
Therefore, the estimated height of the pine tree is 720 inches.
if you guys want the picture, this is the picture link:
www.webassign.net/laratrmrp6/2-1-057-alt.gif
yes. each object is 3 times as tall as its shadow's length.
h/20 = 36/12
h=(36*20)/12
h= 60
is this answer correct