Answer :
Final answer:
The TV with a 30-inch diagonal that forms a 30-60-90 triangle has an exact width of 15 inches and a length of 15√3 inches. The closest answer option provided is d) 15 inches by 15/3 inches, but the precise length should be expressed as 15√3 inches for accuracy.
Explanation:
To determine the length and width of a TV screen with a 30-inch diagonal forming a 30-60-90 right triangle, we use the special ratio for the sides of this type of triangle: the sides opposite the 30°, 60°, and 90° angles are in the ratio of 1: √3: 2, respectively. The diagonal is the longest side, so we can set the hypotenuse (opposite the 90° angle) to 30 inches. Thus, the side opposite the 30° angle (which is the width) is half of the hypotenuse, and the side opposite the 60° angle (which is the length) is the hypotenuse times √3/2. Therefore, the width is 30/2 = 15 inches and the length is 30 * (√3/2) = 15√3 inches ≈ 15 * 1.732 = 25.98 inches.
The correct answer for the dimensions of the TV, given that it forms a 30-60-90 triangle, would be:
- Width: 15 inches
- Length: 15√3 inches
Among the given options, the closest is d) 15 inches by 15/3 inches; however, to be exact, the width is 15 inches, and the length should be expressed as 15√3 inches, not 15/3 inches.
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