Sure, let's solve for the height [tex]\(h\)[/tex] of the flagpole step-by-step.
1. Understand the Problem:
- Kira's height is 5 feet.
- Kira's shadow length is 10 feet.
- The flagpole's shadow length is 28 feet.
- We are to find the height [tex]\(h\)[/tex] of the flagpole.
2. Setting up the Proportion:
We can use the concept of similar triangles to set up a proportion because the triangles formed by Kira and her shadow and the flagpole and its shadow are similar.
The relationship between the heights and the shadows of similar triangles is proportional:
[tex]\[
\frac{\text{Kira's height}}{\text{Kira's shadow length}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow length}}
\][/tex]
3. Substitute the Known Values:
Substituting the values we know:
[tex]\[
\frac{5}{10} = \frac{h}{28}
\][/tex]
4. Solve for [tex]\(h\)[/tex]:
To find the height [tex]\(h\)[/tex] of the flagpole, we can solve for [tex]\(h\)[/tex] by cross-multiplying:
[tex]\[
5 \times 28 = 10 \times h
\][/tex]
Simplify the equation:
[tex]\[
140 = 10h
\][/tex]
Isolate [tex]\(h\)[/tex]:
[tex]\[
h = \frac{140}{10} = 14
\][/tex]
Therefore, the height [tex]\(h\)[/tex] of the flagpole is:
[tex]\[
h = 14 \text{ feet}
\][/tex]
