Trigonometry / Unit 2: Right Triangle Trigonometry
2.3 Finding Missing Sides
Notes
To find a side, pick the ratio that connects the known angle, the known side and the unknown side. Set up an equation and solve.
- Make sure your calculator is in degree mode when the angle is in degrees.
- If the unknown is in the numerator, multiply. If it is in the denominator, divide.
- Example: angle $50^\circ$, hypotenuse 10, find the side opposite: $\displaystyle \sin 50^\circ = \frac{x}{10}$, so $x = 10\sin 50^\circ \approx 7.66$.
Practice
A right triangle has a $35^\circ$ angle and the adjacent leg is 12. About how long is the opposite leg?
$\displaystyle \tan 35^\circ = \frac{x}{12}$, so $x = 12\tan 35^\circ \approx 8.4$.
A right triangle has hypotenuse 20 and a $40^\circ$ angle. About how long is the side opposite the $40^\circ$ angle?
$x = 20\sin 40^\circ \approx 12.86$.
A 15-foot ladder leans against a wall and makes a $70^\circ$ angle with the ground. About how high up the wall does it reach?
The height is opposite the $70^\circ$ angle: $15\sin 70^\circ \approx 14.1$.
Ready for more? Take the Unit 2 test.