1. Right Triangle Trig: Solving for a Missing Side

2. Trigonometric Ratios We define the 3 trigonometric ratios in terms of fractions of sides of right angled triangles.   Hypotenuse (HYP) Adjacent (ADJ) Opposite (OPP)

3. SohCahToa S ine equals O pposite over H ypotenuse C osine equals A djacent over H ypotenuse T angent equals O pposite over A djacent

4. Practice Together: Given each triangle, write the ratio that could be used to find x by connecting the angle and sides given. 65  a x 32  b x

5. YOU DO: Given the triangle, write all the ratios that could be used to find x by connecting the angle and sides given. 56  d x c

6. Steps to finding the missing sides of a right triangle using trigonometric ratios: 1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the given angle 61  9.6 cm x HYP OPP ADJ

7. Steps to finding the missing sides of a right triangle using trigonometric ratios: 2. For the given angle choose the correct trigonometric ratio which can be used to set up an equation 3. Set up the equation 61  9.6 cm x HYP OPP ADJ

8. Steps to finding the missing sides of a right triangle using trigonometric ratios: 4. Solve the equation to find the unknown. 61  9.6 cm x HYP OPP ADJ

9. Practice Together: Find, to 2 decimal places, the unknown length in the triangle. 41  x m 7.8 m

10. YOU DO: Find, to 1 decimal place, all the unknown angles and sides in the triangle.  a m 14.6 m 63  b m

11. Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 20 m x ta n 205 ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

12. Ex: 2 Find the missing side. Round to the nearest tenth. 80 ft x ta n 807272 =  ( ) ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

13. Ex: 3 Find the missing side. Round to the nearest tenth. 283 m x Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

14. Ex: 4 Find the missing side. Round to the nearest tenth. 20 ft x