1. Do Now  Take out your calculator  Take a protractor from the front.  Draw a right triangle DEF with 20 o, 70 o and 90 o angles, respectively. Make sure your sides are straight and your angles are accurate.

2. Solving with Trig Ratios

3. Today’s Objectives  Use the sine, cosine and tangent ratios to solve problems.  Find missing sides and angles.  Apply inverse trigonometry.  Use problem solving skills.

4. Per Request  https://www.youtube.com/watch?v=t2uPYYLH4Zo https://www.youtube.com/watch?v=t2uPYYLH4Zo

5. Investigation 1. Start with your triangle from the Do Now. 2. Measure DE, DF, and EF to the nearest millimeter. 3. Use your side lengths and the definitions of sine, cosine, and tangent to complete this table. Round to four decimals. 4. Share your results with your group. Calculate the average of each ratio within your group. Create a new table with your group’s average values. m<Dsin Dcos Dtan D 20 o m<Esin Ecos Etan E 70 o m<Dsin Dcos Dtan D 20 o m<Esin Ecos Etan E 70 o

6. Investigation  What observations can you make about the trigonometric ratios you found?  What is the relationship between the values for 20 o and the values for 70 o ?  Why do you think these relationships exist?

7. Trig Tables

8. Calculators of 2015  Experiment with your calculator to determine how to find the sine, cosine, and tangent values of angles.  Use your calculator to compare with the trig ratios you found by measuring sides.

9. Example  Find the length of the hypotenuse of a right triangle if an acute angle measures 20 o and the leg opposite the angle measures 410ft. 410 ft 20 o x

10. Example  A right triangle has legs of length 8 inches and 15 inches. Find the measure of the angle opposite the 8-inch leg. 8 in xoxo 15 in

11. Practice

14. Today’s Objectives  Use the sine, cosine and tangent ratios to solve problems.  Find missing sides and angles.  Apply inverse trigonometry.  Use problem solving skills.

15. Exit Slip 1. Find the missing side to the nearest whole cm. 2. Find the perimeter of this right triangle. 85m 35 o 17cm65 o b

16. Honors Exit Slip 1. Find the missing side to the nearest whole cm. 2. Find the perimeter of this rectangle. 85m 35 o 17cm65 o b