Instructions.
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When the angle is \(30^\circ\text{,}\) compare the lengths of the three sides. Which side is the shortest? Which is the longest? How do these side lengths relate to the displayed values of \(\sin 30^\circ\text{,}\) \(\cos 30^\circ\text{,}\) and \(\tan 30^\circ\text{?}\)
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Now move the slider to \(60^\circ\text{.}\) What changes in the triangle? Which sides appear to have exchanged roles compared to the \(30^\circ\) case?
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Compare \(\sin 30^\circ\) with \(\cos 60^\circ\text{.}\) What do you notice? Why might these values be the same?
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Compare \(\cos 30^\circ\) with \(\sin 60^\circ\text{.}\) What pattern do you observe?
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How does the tangent value change between \(30^\circ\) and \(60^\circ\text{?}\) What does this tell you about the ratio of opposite to adjacent sides?
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Based on your observations, what relationship can you describe between complementary angles (angles that add up to \(90^\circ\))?
Discuss your findings with a partner and explain how the geometry of the triangle supports the calculator values.