Proportion - If a 30-foot tree cast an 18-foot shadow, find the length of the shadow cast by a 24-foot tree.
14.4ft.
1. on a trip to washington dc, you and your friend are standing next to the washington monument. your friend want to buy a guide book to find out how tall the washington monument is, but will use the money to buy a snack to share instead if you can figure it out. if you know your own height, what two additional measurements must you know to solve the problem?
THE LENGTH OF YOUR SHADOW AND THE LENGTH OF THE SHADOW CAST BY THE WASHINGTON MONUMENT
2. if a 30-foot tree casts an 80-foot shadow, find the length of the shadow cast by a 24-foot tree.
14.4 FEET
3. determine whether the triangles are similar. if so, name the similar triangles. YES, THE TRIANGLES ARE SIMILAR. PSQ ~ RST
4. is the following solution for the value of x in the figure correct or incorrect? explain. 4/8 = 15/x, x = 30
THE SOLUTION FOR THE VALUE OF X IS INCORRECT BECAUSE THE PROPORTION DOES NOT USE THE RATIOS OF CORRESPONDING SIDES
5. in abc, m<a=42°, m<b=50°, ab=4, and ac=3. in xyz, m<x=42°, m<z=88°, xy=14, and yz=9.5. find the measures of bc and xz. round to one decimal place.
BC = 2.7, XZ = 10.5
Cross multiply and solve for x.
30/18 = 24/x
31.5/17.5=7.5/x
To find the length of the shadow cast by a 24-foot tree, we can use the concept of proportions. Proportions are equations that show the equality of two ratios.
In this case, we can set up a proportion between the height of the trees and the length of their shadows. Let's represent the height of the first tree as h₁ and the length of its shadow as s₁, and similarly, the height of the second tree as h₂ and the length of its shadow as s₂.
The proportion between the two trees' heights and their respective shadow lengths can be written as:
h₁ / s₁ = h₂ / s₂.
We know that the height of the first tree (h₁) is 30 feet and its shadow length (s₁) is 18 feet. We need to find the shadow length of the second tree (s₂) when its height (h₂) is 24 feet. We can plug the known values into the proportion and solve for s₂:
30 / 18 = 24 / s₂.
To isolate s₂, we can cross-multiply:
30 * s₂ = 18 * 24.
Now, divide both sides of the equation by 30 to solve for s₂:
s₂ = (18 * 24) / 30.
Calculating this expression gives us:
s₂ = 432 / 30 = 14.4 feet.
Therefore, the length of the shadow cast by a 24-foot tree would be approximately 14.4 feet.