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

1. 1. The ratios for \(\sin 30˚\) are the same for any triangle:  \(\sin 30˚=\dfrac{1}{2}\); the ratios for \(\sin 60˚\) are the same for any triangle: \(\sin 60˚=\dfrac{\sqrt 3}{2}\); and the ratios for \(\sin 45˚\) are the same for any triangle:  \(\sin 45˚= \dfrac{1}{\sqrt 2}\).
   2. The ratios for \(\cos 30˚\) are the same for any triangle: \(\cos 30˚=\dfrac{\sqrt 3}{2}\); the ratios for \(\cos 60˚\) are the same any triangle: \(\cos 60˚= \dfrac{1}{2}\); and the ratios for \(\cos 45˚\) are the same for any triangle:  \(\cos 45˚= \dfrac{\sqrt 2}{2}\).
   3. The ratios for \(\tan 30˚\) are the same for any triangle: \(\tan 30˚=\dfrac{3\sqrt3}{3}\); the ratios for \(\tan 60˚\) are the same any triangle: \(\tan 60˚= \sqrt 3\); and the ratios for \(\tan 45˚\) are the same for any triangle:  \(\tan 45˚= 1\).
   4. The ratios for \(\tan 30˚\) and \(\tan 60˚\) are reciprocals for any triangle:  \(\tan 30˚ = \dfrac1{\tan 60˚}\).
   5. The sine of an angle and the cosine of its complement are the same: \(\sin 30˚ = \cos 60˚\); and \(\sin 60˚ = \cos 30˚\).
   6. The sine and cosine of 45˚ are the same: \(\sin 45˚ = \cos45˚=1\).

---

Return to Try This! (Ratios for Special Right Triangles)

Go to Practice (Finding Triangle Parts)