Geometry / Unit 9: Right Triangles and Trigonometry
9.6 Solving Right Triangles
Notes
To find an angle, use an inverse trig function: $\sin^{-1}$, $\cos^{-1}$ or $\tan^{-1}$.
- If $\displaystyle \tan A = \frac{3}{4}$, then $\displaystyle m\angle A = \tan^{-1}\left(\frac{3}{4}\right) \approx 36.9^\circ$.
- To solve a right triangle, find all missing sides and angles.
- The two acute angles add to $90^\circ$.
Practice
A right triangle has legs 5 and 12. Find the angle opposite the leg of 5, to the nearest tenth.
$\displaystyle \tan^{-1}\left(\frac{5}{12}\right) \approx 22.6^\circ$.
A right triangle has a hypotenuse of 10 and a leg of 7 opposite angle $A$. Find $m\angle A$ to the nearest tenth.
$\sin^{-1}(0.7) \approx 44.4^\circ$.
In right $\triangle ABC$ with right angle $C$, $m\angle A = 28^\circ$. Find $m\angle B$.
$90 - 28 = 62$.
Ready for more? Take the Unit 9 test.