Integrated Math 2 / Unit 7: Right Triangle Trigonometry
7.4 Finding Missing Sides
Notes
Use the trig ratio that connects the side you know and the side you want. Make sure your calculator is in degree mode.
- Choose: opposite and hypotenuse, use sine; adjacent and hypotenuse, use cosine; opposite and adjacent, use tangent.
- Example: hypotenuse 20 and angle $35°$, find the opposite side. $\displaystyle \sin 35° = \frac{x}{20}$, so $x = 20 \sin 35° \approx 11.5$.
- Multiply when the unknown is in the numerator. Divide when it is in the denominator.
Practice
Find the side adjacent to a $40°$ angle in a right triangle with hypotenuse 10.
$\displaystyle \cos 40° = \frac{x}{10}$, so $x = 10 \cos 40° \approx 7.7$.
A right triangle has an angle of $52°$ and an adjacent side of 15. Find the opposite side.
$\displaystyle \tan 52° = \frac{x}{15}$, so $x = 15 \tan 52° \approx 19.2$.
The hypotenuse is 20 and one angle is $35°$. Find the side opposite that angle.
$\displaystyle \sin 35° = \frac{x}{20}$, so $x = 20 \sin 35° \approx 11.5$.
Ready for more? Take the Unit 7 test.