Let's determine the dimensions of a TV with a 28-inch diagonal, assuming it forms a pair of 30-60-90 right triangles.
Step-by-Step Solution:
1. Understanding a 30-60-90 Triangle:
In a 30-60-90 triangle, the sides have the following relationships:
- The side opposite the 30-degree angle is half of the hypotenuse.
- The side opposite the 60-degree angle is [tex]\(\frac{\sqrt{3}}{2}\)[/tex] times the hypotenuse.
2. Given Information:
- Diagonal of the TV (hypotenuse of the 30-60-90 triangles): 28 inches.
3. Calculating the Length (Side Opposite the 30-Degree Angle):
Since the side opposite the 30-degree angle is half of the hypotenuse:
[tex]\[
\text{Length} = \frac{1}{2} \times \text{Diagonal} = \frac{1}{2} \times 28 = 14 \text{ inches}.
\][/tex]
4. Calculating the Width (Side Opposite the 60-Degree Angle):
Since the side opposite the 60-degree angle is [tex]\(\frac{\sqrt{3}}{2}\)[/tex] times the hypotenuse:
[tex]\[
\text{Width} = \frac{\sqrt{3}}{2} \times \text{Diagonal} = \frac{\sqrt{3}}{2} \times 28 = 14\sqrt{3}\text{ inches}.
\][/tex]
Therefore, the exact length and width of the TV are 14 inches and 14[tex]\(\sqrt{3}\)[/tex] inches, respectively.
Conclusion:
The correct answer is:
[tex]\[ \boxed{\text{C. } 14 \text{ inches by } 14\sqrt{3} \text{ inches}}. \][/tex]
