Integrated Math 2 / Unit 7: Right Triangle Trigonometry
7.5 Finding Missing Angles
Notes
Use an inverse trig function to find an angle from a ratio: $\sin^{-1}$, $\cos^{-1}$, $\tan^{-1}$.
- If $\sin\theta = 0.6$, then $\theta = \sin^{-1}(0.6) \approx 36.9°$.
- Pick the ratio from the two sides you know.
- The two acute angles add to $90°$.
- Example: opposite 5, adjacent 12: $\displaystyle \tan\theta = \frac{5}{12}$, so $\theta \approx 22.6°$.
Practice
In a right triangle the side opposite angle $\theta$ is 5 and the adjacent side is 12. Find $\theta$.
$\displaystyle \tan\theta = \frac{5}{12} \approx 0.4167$, so $\theta = \tan^{-1}(0.4167) \approx 22.6°$.
The side opposite angle $\theta$ is 6 and the hypotenuse is 10. Find $\theta$.
$\sin\theta = 0.6$, so $\theta \approx 36.9°$.
The side adjacent to angle $\theta$ is 9 and the hypotenuse is 15. Find $\theta$.
$\displaystyle \cos\theta = \frac{9}{15} = 0.6$, so $\theta \approx 53.1°$.
Ready for more? Take the Unit 7 test.