Geometry / Unit 9: Right Triangles and Trigonometry
9.5 Sine, Cosine and Tangent
Notes
For an acute angle $A$ in a right triangle, the trig ratios compare sides. Remember SOH-CAH-TOA.
- $\displaystyle \sin A = \frac{\text{opposite}}{\text{hypotenuse}}$, $\displaystyle \cos A = \frac{\text{adjacent}}{\text{hypotenuse}}$, $\displaystyle \tan A = \frac{\text{opposite}}{\text{adjacent}}$.
- Cofunctions: $\sin A = \cos(90^\circ - A)$.
- To find a side, write the ratio and solve. Use degree mode on a calculator.
- Example: angle $30^\circ$, hypotenuse 20. Opposite $= 20 \sin 30^\circ = 10$.
Practice
In $\triangle ABC$, $\angle C$ is a right angle, $AC = 8$, $BC = 15$ and $AB = 17$. Find $\sin A$.
The side opposite $\angle A$ is $BC = 15$ and the hypotenuse is 17.
A right triangle has a $35^\circ$ angle. The leg adjacent to it is 20. Find the opposite leg to the nearest tenth. ($\tan 35^\circ \approx 0.7002$)
Opposite $= 20 \tan 35^\circ \approx 14.0$.
Which expression equals $\sin 40^\circ$?
Cofunctions: $\sin A = \cos(90^\circ - A)$.
Ready for more? Take the Unit 9 test.