Trigonometry / Unit 2: Right Triangle Trigonometry
2.4 Finding Missing Angles
Notes
When two sides are known, use an inverse trig function ($\sin^{-1}$, $\cos^{-1}$, $\tan^{-1}$) to find the angle.
- If $\displaystyle \tan\theta = \frac{6}{8}$, then $\theta = \tan^{-1}(0.75) \approx 36.9^\circ$.
- The two acute angles of a right triangle add up to $90^\circ$.
- To solve a right triangle means to find all missing sides and angles.
- If your answer looks tiny like $0.6$, check that the calculator is in degree mode.
Practice
A right triangle has legs 6 and 8. What is the angle opposite the leg of length 6, to the nearest tenth of a degree?
$\displaystyle \tan\theta = \frac{6}{8}$, so $\theta = \tan^{-1}(0.75) \approx 36.9^\circ$.
In a right triangle, $\theta$ is acute, the hypotenuse is 13 and the leg adjacent to $\theta$ is 5. What is $\theta$ to the nearest tenth of a degree?
$\displaystyle \cos\theta = \frac{5}{13}$, so $\displaystyle \theta = \cos^{-1}\left(\frac{5}{13}\right) \approx 67.4^\circ$.
One acute angle of a right triangle is $28^\circ$. What is the other acute angle?
The acute angles add to $90^\circ$.
Ready for more? Take the Unit 2 test.