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# Hprec6 2

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### Hprec6 2

1. 1. 6-2: Trignometric Applications © 2007 Roy L. Gover (www.mrgover.com) Learning Goals: •Solve applications using triangles •Solve triangles using trigonmetric ratios
2. 2. Important Idea Triangle Sum Theorem: The sum of the measures of the angles in a triangle is 180°. Pythagorean Theorem: In a right triangle with legs a and b and hypotenuse c, a2 +b2 =c2
3. 3. Important Idea For any two triangles with congruent angles, regardless of size, the ratio of corresponding sides are equal. y y’ r r’ x x’
4. 4. Example α 17 cm.8 cm. 15 cm. Find the values of the 6 trig functions of . Leave your answers as a fraction. α
5. 5. Try This β 13 cm. 5 cm. 12 cm. Find the values of the 6 trig functions of . Leave your answers as a fraction. β
6. 6. Solution 12 sin 13 5 cos 13 12 tan 5 β β β = = = 13 csc 12 13 sec 5 5 cot 12 β β β = = =
7. 7. Example A BC 12 52°15’ b c Solve triangle ABC. Round angle & side measures to the nearest tenth.
8. 8. Example A BC 12 52°15’ b c Step 1: Draw & label Step 2: Solve for the missing angle Step 3: Write trig equations & solve for the missing sides
9. 9. Try This A B C 7 49°12’ b c Solve triangle ABC. Round angle and side measures to the nearest tenth.
10. 10. Solution A B C 7 49°12’ b c C=90° B =40.8° c ≈ 9.2 b ≈ 6.0
11. 11. Definition Inverse Trig Function: the function that gives the angle whose trig value is known. Inverse trig functions are known as an arc or inverse function.
12. 12. Example Find an angle whose sin is . θ Stated another way: Find when 2 sin 2 θ = 2 2
13. 13. Definition The inverse trig functions are: 1 1 1 sin cos tan x x x θ θ θ − − − = = = arcsin arccos arctan x x x θ θ θ = = = or
14. 14. Example Stated another way: Find the angle whose cos is .523. Find (arccos . 523) 1 cos .523−
15. 15. Try This Find . State your answer in degrees to the nearest tenth. 51.1° 1 tan 1.2382−
16. 16. Example T R S 12 In triangle TRS, find the measure of angle T in degrees to the nearest tenth.. 5
17. 17. Try This T R S 12 10 In triangle TRS, find the measure of angle T in degrees to the nearest tenth. Don’t forget to check “mode”. 33.6°
18. 18. ExampleA 16 foot ladder is placed against the side of a house. The base of the ladder makes a 60° angle with the ground. How far up the side of the house will the ladder reach?
19. 19. ExampleA ladder reaches 17 feet up the side of a house. If the base of the ladder makes an angle of 62° with the ground, how long must the ladder be?
20. 20. ExampleA 25 foot ladder reaches 20 feet up the side of a house. What is the angle the ladder makes with the ground?
21. 21. Example Commercial airliners fly at an altitude of 30,000 feet. They start descending toward the airport when they are far away so they will not have to dive at a steep angle to land.
22. 22. Example 1. If the pilot wants the plane to descend at an angle of 3°, at what horizontal distance from the airport must she start her descent?
23. 23. Example 2. If she starts descending 170.5 miles (900,000 feet) from the airport, what angle will the plane make with the horizontal?
24. 24. ExampleWhat is the tallest building a ladder truck can reach if the angle of the ladder is 60°, the length of the ladder is 108 ft. and the ladder is mounted on the truck 8 ft. from the ground.
25. 25. Try This The sun casts a shadow 176 ft. long when it shines over a flagpole with an angle of elevation of 20°. What is the height of the flagpole?
26. 26. Solution 1. Draw & label: 20° 176 ft x 2. Write an equation & solve 64.1 ft.
27. 27. Try This A girl spots a tree with an angle of elevation of 25° the tree and an angle of depression of 15° to the bottom of the tree from eye level. Her eye level is 165 cm. How far is the girl from the tree? How high is the tree? to the top of
28. 28. Try This 25° 15° 165cm Distance to tree: 615.8 cm Height of tree: 452.2 cm
29. 29. Lesson Close On a sheet of paper, make up a right triangle problem and solve it. Draw & label a sketch, show all your work and circle your answer.