Discovering the Trig Ratios
In this activity we are going to explore the ratios between side lengths of similar right angled triangles.
Calculate the ratio of the length of the Opposite side to the length of the Adjacent side (that is work out Opposite / Adjacent).
Move the red point to create a similar triangle.
Why is the new triangle similar to the original?
Calculate the same ratio of Opposite to Adjacent.
Create another similar triangle, and again calculate the ratio of Opposite to Adjacent.
What do you notice?
Now create a new triangle, by pressing the button, and repeat the process for this new triangle.
Why is this triangle NOT similar to the previous ones?
Describe what you have found.
Now repeat the whole process, but finding the ratio of Opposite to Hypotenuse and then the ratio Adjacent to Hypotenuse.
Calculate the ratio of the length of the Opposite side to the length of the Adjacent side (that is work out Opposite / Adjacent).
Move the red point to create a similar triangle.
Why is the new triangle similar to the original?
Calculate the same ratio of Opposite to Adjacent.
Create another similar triangle, and again calculate the ratio of Opposite to Adjacent.
What do you notice?
Now create a new triangle, by pressing the button, and repeat the process for this new triangle.
Why is this triangle NOT similar to the previous ones?
Describe what you have found.
Now repeat the whole process, but finding the ratio of Opposite to Hypotenuse and then the ratio Adjacent to Hypotenuse.
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