a person who is 1.9m tall has a shadow that is 1.5m long. at the same time a flagpole has a shadow that is 8m long. determine the height of the flagpole to the nearest tenth of a metre. draw a diagram
Use a proportion. Cross multiply and solve for x.
1.9/1.5 = x/8
10.13
To determine the height of the flagpole, we can use the concept of similar triangles.
Step 1: Draw a diagram:
Let's draw a diagram to visualize the scenario. The person standing upright will have a shadow, and there will be a flagpole with its respective shadow.
Person (P) Flagpole (F)
|______________|
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\|
S (Shadow)
Step 2: Identify the given information:
- The person's height (P) is given as 1.9m, and their shadow (S) is given as 1.5m.
- The flagpole's shadow (S) is given as 8m.
Step 3: Set up the proportion:
We can set up a proportion using the ratios between the corresponding sides of the two similar triangles:
Height of person / Length of person's shadow = Height of flagpole / Length of flagpole's shadow
1.9m / 1.5m = Height of flagpole / 8m
Step 4: Solve for the height of the flagpole:
We can simplify the proportion and solve for the height of the flagpole:
(1.9m * 8m) / 1.5m = Height of flagpole
15.2m / 1.5m = Height of flagpole
10.13m = Height of flagpole (rounded to the nearest tenth of a meter)
Therefore, the height of the flagpole is approximately 10.1 meters.
To determine the height of the flagpole, we can set up a proportion using the similar triangles formed by the person and their shadow, as well as the flagpole and its shadow.
Let's label the height of the flagpole as 'x.' The person's height is given as 1.9m with a corresponding shadow of 1.5m. The flagpole's shadow is given as 8m.
We can set up the following proportion:
(person's height) / (person's shadow) = (flagpole's height) / (flagpole's shadow)
1.9m / 1.5m = x / 8m
Now, we can solve this proportion to find the height of the flagpole.
1.9m * 8m = 1.5m * x
15.2m = 1.5m * x
To isolate 'x,' divide both sides of the equation by 1.5m:
15.2m / 1.5m = x
x ≈ 10.1m
Therefore, the height of the flagpole is approximately 10.1 meters.
Here's a diagram to help visualize the situation:
A
|
|
|------------> (person)
|
| B
_________
| |
| flagpole |
|________________|
In the diagram:
- Point A represents the person.
- The line from point A to the right side represents the shadow of the person.
- Point B represents the top of the flagpole.
- The line from point B to the right side represents the shadow of the flagpole.