High School: Geometry
Similarity, Right Triangles, and Trigonometry HSG-SRT.C.8
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
On the one hand, your students know the basic trigonometric ratios like the back of their hands. And on the other hand, they could use the Pythagorean theorem with one hand tied behind their backs. Now, it's time for them to put their hands together and use the two concepts to solve applications or word problems.
This standard focuses on having students apply their knowledge of trig ratios and the Pythagorean theorem to solve problems other than the usual, "Find the missing angle/side." Often, they'll find it helpful to draw a model or visually represent the given information in order to organize their thoughts and clearly show their work. This often involves creating and solving mathematical models.
And how, exactly, will students achieve and demonstrate mastery in regards to this standard? Give them plenty of word problems or applications to solve using trig ratios and the Pythagorean theorem. Challenge them to come up with their own problems for their peers to solve. Encourage them to find examples from their own lives of problems that can be solved with these concepts.
With enough practice solving applied problems, your students will start to see right triangles and trig functions everywhere. (We mean that figuratively. If they really do see right triangles and trig functions everywhere, they should consult an optometrist.)