When introducing Trigonometry I usually ensure students draw and measure right triangles using any of the similar triangle properties. I then ask them to look for pattens w.r.t. ratio of sides. But if I fall short of time I’ll show them these three triangles and ask what they have in common.
Students spot that they are similar triangles (AA) and the ratio of height to the diagonal is 1:2 (this would be the good time to introduce the terminology opp: hyp w.r.t angle 30).
Then I’ll show them the triangle below and ask for the length of the hypotenuse. I want them to realize that because it is similar (AA) to the three triangles above, we know that ratio of opp: hyp is 1:2, hence the length of the hypotenuse must be 70.
Please comment below if you have any other idea of introducing …..
I’m also including ‘Introduction to Trigonometry’ from ‘Project math’. If time permits, I think it’s the best way to introduce the lesson. Students will have hands – on experience and would enjoy the lesson.