To find the height of the Ferris wheel using the information provided, we can use the concept of similar triangles. Here are the steps to solve this problem:
1. Convert Saad's height from inches to feet:
- Saad's height in feet is [tex]\( \frac{81}{12} \)[/tex] feet.
- Calculation: [tex]\( \frac{81}{12} = 6.75 \)[/tex] feet.
2. Set up the proportion using similar triangles:
- The length of Saad's shadow is 5 feet.
- The length of the Ferris wheel's shadow is 30 feet.
- Since the sun's rays are parallel, the ratio of the height of Saad to the length of his shadow will be the same as the ratio of the height of the Ferris wheel to the length of its shadow.
[tex]\[
\frac{\text{Saad's height}}{\text{Saad's shadow length}} = \frac{\text{Ferris wheel's height}}{\text{Ferris wheel's shadow length}}
\][/tex]
[tex]\[
\frac{6.75 \, \text{ft}}{5 \, \text{ft}} = \frac{\text{Ferris wheel's height}}{30 \, \text{ft}}
\][/tex]
3. Solve the proportion for the height of the Ferris wheel:
- Let [tex]\( h \)[/tex] represent the height of the Ferris wheel in feet.
[tex]\[
\frac{6.75}{5} = \frac{h}{30}
\][/tex]
Cross-multiplying to solve for [tex]\( h \)[/tex]:
[tex]\[
6.75 \times 30 = 5 \times h
\][/tex]
[tex]\[
202.5 = 5h
\][/tex]
[tex]\[
h = \frac{202.5}{5} = 40.5 \, \text{feet}
\][/tex]
4. Convert the height of the Ferris wheel from feet to inches:
- There are 12 inches in a foot.
- So, the height of the Ferris wheel in inches is:
[tex]\[
40.5 \, \text{ft} \times 12 \, \frac{\text{in}}{\text{ft}} = 486 \, \text{inches}
\][/tex]
5. Choose the correct answer option:
- Option C: 40
Therefore, the height of the Ferris wheel is [tex]\( \boxed{40} \)[/tex] feet.
