Define and calculate the sine of angles in right triangles. Use similarity criteria to generalize the definition of sine to all angles of the same measure.
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Below is a set of similar right triangles. Find the ratio of the side lengths within each triangle that describe the side opposite the marked angle divided by the hypotenuse.
What is the sine of 0°, 45°, 60°, and 90°?
$${\triangle ABC}$$ is a right triangle. What is the sine of $${\angle BAC}$$?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Explain how you know that the following statement is always, sometimes, or never true:
“You can find the sine of any angle in any triangle by finding the ratio of the length of the opposite side over the length of the hypotenuse.”
Find the sine of each angle shown in the diagram below. Then, predict between which two benchmark angle measures the angles fall between based on the sine.