GEOM 2 | Lesson 4 | Try This! (Trig Ratios for Special Right Triangles)

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°
  1. Calculate the sine, cosine, and tangent ratios for all five triangles.
  2. Which ratios are the same across multiple triangles?
  3. Which ratios are reciprocals?
  4. Write several statements to summarize the connections between the ratios.

Check solution to #4 here.

Go to Practice (Finding Triangle Parts)

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