1. Section 4.1 Right Triangle Trigonometry

2. Find values of trigonometric functions for acute angles of right triangles. Solve right triangles. Mastery Objectives

3. Balloons  Large helium-filled balloons are a tradition of many holiday parades. Long cables attached to the balloon are used by volunteers to lead the balloon along the parade route. Suppose two of the cables are attached to a balloon at the same point, and the volunteers holding these cables stand so that the ends of the cables lie in the same vertical plane. If you know the measure of the angle that each cable makes with the ground and the distance between the volunteers, you can use right triangle trigonometry to find the height of the balloon above the ground.

4. Trigonometry  Means “Triangle Measure”  In this lesson we study right triangle trigonometry  Using the side measures of a right triangle and a reference angle labeled θ (Greek letter theta), we can form the trigonometric ratios that define six trigonometric functions.

5. Trigonometric Functions

6. Reciprocal and Quotient Functions

7. Find the exact values of the six trigonometric functions of θ.

9. If find the exact values of the five remaining trigonometric Functions for the acute angle .

10. Solution Answer:

12. Special Right Triangles  You will often be asked to find the trig functions of specific acute angle measures. The common angle measures are 30º, 60º, and 45º.  To remember the values, you can use the properties of 30º-60º-90º ∆s and 45º-45º- 90º ∆s.

13. Warm Up

14. Special Ratios to Memorize

15. Trig Values of Special Angles

16. Solving Right Triangles  Trigonometric functions can be used to find missing side lengths and angle measures of right triangles.

17. Find the value of x. Round to the nearest hundredth, if necessary. Answer: about 5.7

18. Find the value of x. Round to the nearest hundredth, if necessary. A.4.6 B.8.1 C.9.3 D.10.7

19. Ernie is walking along the course x, shown. Find the distance he must walk. A.569.7 ft B.228.0 ft C.69.5 ft D.8.5 ft

20. A competitor in a hiking competition must climb up the inclined course as shown to reach the finish line. Determine the vertical distance in feet that the competitor will climb to reach the finish line. (Hint: 1 mile = 5280 feet.) Then find the distance he will climb. Answer:about 5864 ft

21. Inverse Trig Functions When a trigonometric value of an acute angle is known, the corresponding inverse trigonometric function can be used to find the measure of the angle.

22. Use a trigonometric function to find the measure of θ. Round to the nearest degree, if necessary. Answer:about 50°

23. Use a trigonometric function to find the measure of Ө. Round to the nearest degree, if necessary. A.32° B.40° C.50° D.58°

24. Angles of Elevation and Depression  An angle of elevation is the angle formed by a horizontal line and an observer’s line of sight of an object above. An angle of depression is the angle formed by a horizontal line and an observer’s line of sight to the object below.

25. The chair lift at a ski resort rises at an angle of 20.75° while traveling up the side of a mountain and attains a vertical height of 1200 feet when it reaches the top. How far does the chair lift travel up the side of the mountain? Answer: about 3387 ft

26. A person on an airplane looks down at a point on the ground at an angle of depression of 15°. The plane is flying at an altitude of 10,000 feet. How far is the person from the point on the ground to the nearest foot? A.2588 ft B.10,353 ft C.37,321 ft D.38,637 ft

27. Solve ΔFGH. Round side lengths to the nearest tenth and angle measures to the nearest degree. Answer:H ≈ 49°, f ≈ 18.5, h ≈ 21.0

28. Solve ΔABC. Round side lengths to the nearest tenth and angle measures to the nearest degree. Answer:a = 10.3, B ≈ 29°, C ≈ 61°

29. A.a ≈ 44.9, b ≈ 82.7, A = 36° B.a ≈ 40.3, b ≈ 82.7, A = 26° C.a ≈ 40.3, b ≈ 85.4, A = 26° D.a ≈ 54.1, b ≈ 74.4, A = 36° Solve ΔABC. Round side lengths to the nearest tenth and angle measures to the nearest degree.

30. Homework Pg. 227: 1, 2, 4, 5, 8, 9, 12, 19, 20, 23, 27, 28, 31, 32, 36, 39, 45, 47, 48