1. Right Triangle Trigonometry Find the value of trigonometric functions of acute angles Use the complementary angle theorem Solve right triangles Solve applied

2. Right Triangles A triangle in which one angle is a right angle is called a right triangle Opposite Side Hypotenuse Adjacent Side

3. Pythagorean Theorem a 2 + b 2 = c 2 c b a

4. Trigonometric Functions

5. Complementary Angles: Co-functions of complementary angles are equal sin 30° = cos 60° tan 40° = cot 50° sec 80° = csc 10°

6. Solving Right triangles To solve a right triangle means to find the missing lengths of its sides and the measurements of its angles

7. Solving a right triangle Use the figure. If b=2 and α = 40°, find a, c and β. c a 2 40 °

8. Finding the width of a river A surveyor can measure the width of a river by setting up a transit at a point C on one side of the river and taking a sighting of a point A on the other side. After turning through an angle of 90 ° at C, the surveyor walks a distance of 200 meters to point B. Using the transit at B, the angle β is measured and found to be 20°. What is the width of the river rounded to the nearest meter?

9. Work and Diagram

10. Finding the inclination of a mountain trail A straight trail leads from the Alpine Hotel, elevation 8000 ft, to a scenic overlook, elevation 11,100 feet. The length of the trail 14,100 feet. What is the inclination (grade) of the trail? That is what is the angle β

11. Angle of elevation and depression Vertical heights can sometimes be measured using either the angle of elevation or the angle of depression. Angle of elevation Angle of depression

12. Classwork and Homework Page 491 examples 9-13, 29-31, 50-56