The diagonal of a TV is 30 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the TV?

1) 15.2 inches by 15.2 inches
2) 60 inches by \(\frac{60}{3}\) inches
3) 60.2 inches by \(\frac{60.2}{2}\) inches
4) 15 inches by \(\frac{15}{\sqrt{3}}\) inches

In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the shorter leg. Given a TV diagonal of 30 inches, the TV's dimensions are approximately 15 inches (height) by 26 inches (width).

Explanation:

In a 30-60-90 triangle, the length of the hypotenuse (the diagonal of the TV) is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg. Given that the diagonal of the TV is 30 inches, the shorter leg (usually the height of the TV) becomes 30/2 = 15 inches, and the longer leg (usually the width of the TV) is 15√3 inches.

By simplifying, the width becomes approximately 15 * 1.732 = 25.98 inches. Therefore, the dimensions of the TV are approximately 15 inches (height) by 26 inches (width) according to the 30-60-90 triangle rules.

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