Trig Ratios for Special Right Triangles
Given three 30-60-90 and two 45-45-90 triangles with one side equal to one unit.
Use the table below to record your responses to the following questions.
| Triangle Description | Angle \(\theta\) | sin \(\theta\) | cos \(\theta\) | tan \(\theta\) |
| height = 1 | 30° | |||
| height = 1 | 60° | |||
| base = 1 | 30° | |||
| base = 1 | 60° | |||
| hyp = 1 | 30° | |||
| hyp = 1 | 60° | |||
| legs = 1 | 45° | |||
| legs = \(\dfrac{1}{\sqrt{2}}\) | 45° |
- Calculate the sine, cosine, and tangent ratios for all five triangles.
- Which ratios are the same across multiple triangles?
- Which ratios are reciprocals?
- Write several statements to summarize the connections between the ratios.
