If the sin of angle \( x \) is \( \frac{4}{5} \) and the triangle was dilated to be two times as big as the original, what would be the value of the sin of \( x \) for the dilated triangle? Clue: Use the slash symbol ( \( / \) ) to represent the fraction bar, and enter the fraction with no spaces. Answer for Blank 1:

The value of \( \sin x \) for the dilated triangle remains the same at \( \frac{4}{5} \). When a triangle is dilated, the ratios of the sides—and thus the trigonometric functions—stay unchanged. So, you can focus on the same angle measurement without worrying about the triangle's size! If you're interested in how dilation affects triangles, it’s fascinating! Dilation keeps angles constant while changing the lengths of the sides proportionally. This means all the trigonometric functions based on those angles, like sine, cosine, and tangent, remain unaltered, making your calculations much simpler!