Instructions.
Use this interactive board to explore the relationship between the angle and the sides of the right-angled triangles:
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Adjust the Angle: Drag the \(\theta\) slider. As the angle changes, what happens to the lengths of the opposite sides and the hypotenuses of the three triangles?
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Change Triangle Sizes: Slide points \(A\text{,}\) \(B\text{,}\) and \(C\) horizontally. How does resizing the base (adjacent side) of the triangle affect the lengths of the other two sides?
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Explore the Sine Ratios: Look at the left column of calculations below the graph. Try moving points \(A\text{,}\) \(B\text{,}\) and \(C\) while keeping the angle constant. What do you notice about the ratio of the Opposite side divided by the Hypotenuse? How does this value compare to the sine of \(\theta\) calculated at the top?
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Explore the Cosine Ratios: Now look at the right column. When you change the angle \(\theta\text{,}\) how does the ratio of the Adjacent side divided by the Hypotenuse change? Does dragging points \(A\text{,}\) \(B\text{,}\) or \(C\) to change the size of the triangles alter this ratio?