Trigonometry.pptx
- 1. REAL-LIFE PROBLEMS INVOLVING RIGHT TRIANGLES 9th Grade BY: QUARTER 4 Math Teacher
- 8. Trigonometric ratios Sin θ Opposite side of θ/Hypotenuse Cos θ Adjacent side of θ/Hypotenuse Tan θ Opposite side of θ/Adjacent side of θ Cot θ Adjacent side of θ/Opposite Side of θ Sec θ Hypotenuse/Adjacent side of θ Cosec θ Hypotenuse/Opposite side of θ The six ratios are: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec) and secant (sec)≈
- 10. OBJECTIVES: At the end of the lesson, you are able to: A. Recall the concept of trigonometric ratio, angle of elevation and angle of depression; B. Uses trigonometric ratios to solve real-life problems involving right triangles (M9GE-IVe-1); and C. Solve real – life problems involving angle of elevation and angle of depression.
- 11. Introduction The concepts on trigonometric ratios and angles of elevation and depression are necessary in solving word problems involving right triangles. Many real-life problems involving right triangles are based on these concepts.
- 12. VIDEO DISCUSSION
- 13. Activity 1: Accessibility The Philippines’ Accessibility Law or Batas Pambansa 344 (BP 344) provides regulations designed to make public buildings accessible to all. Under this act, the slope of a ramp designed for those with mobility disabilities must not exceed a 1:12 ratio. This means that for every 12 units of horizontal run, the ramp can rise or fall not more than 1 unit. A ramp forms a right triangle when viewed from the side. WHAT’S NEW?
- 14. A person on a lake sees a plane flying overhead. The angle formed by his line of sight to the plane is 390. if the plane is flying about 5000 ft., find the horizontal ground distance between the person and the plane. ILLUSTRATIVE EXAMPLE #1
- 16. ILLUSTRATIVE EXAMPLE #2 A seesaw has a plank of 4.5 𝑚 long which is supported by a pivot at its center and moves in a vertical plane above the pivot. If the height of the pivot pillar above the ground is 1 𝑚, through what maximum angle can the seesaw beam move?
- 20. RUBRICS
- 21. Finding practical applications of concepts and skills in daily living! Question: 1. Is it important to adopt a procedure in solving problems involving right triangles using trigonometric ratios? Why? 2. How can this concept on trigonometric ratios and solving right triangles be used to solve real-life problems?
- 22. GENERALIZATION How to solve problems involving right triangles?
- 24. Assessment Directions: Read and analyze the problems carefully and choose the letter that corresponds to your answer. Write your answer on a separate sheet.
- 25. Assessment 1. A kite in the air has its 60 m string to the ground and makes an angle of elevation of 45o. About how high is the kite with the ground? a.28.1 m b.31.4 m c.39.7 m d.42.4 m
- 26. Assessment For items 2 to 3, refer to the problem below. A tree that was broken by a string wind brought by the typhoon has its top touch the ground 13 m from the base. It makes an angle with the ground measuring 29o.
- 27. Assessment 2. If y is the height of the broken tree left standing vertically on the ground, which equation will help you find its height? a.Sin 290 = y/13 b.Cos 290 = 13/y c.Tan 290 = y/13 d.Sec 290 = 13/y
- 28. Assessment 3. How tall was the tree before it was broken? a.19.8 m b.22.1 m c.33.7 m d.41.2 m
- 29. Assessment For items 4 to 5, refer to the problem below. To measure the width of the river, a surveying technique is used. Suppose a stake is planted across opposite sides of the river and an angle of 82° at a distance 50 𝑚 to the left of the stake is measured between two stakes.
- 30. Assessment 4. If w represents the width of the river, which equation will help you solve the given problem? a.Sin 82o = w/50 b.Cos 82o = 50/w c.Tan 82o = w/50 d.Sec 82o = 50/w
- 31. Assessment 5. Find the width of the river a.252 m b.355.8 m c.430.2 m d.451.7 m
- 33. ASSIGNMENT The basketball ring is 10 ft. above the ground. The free throw is 15 ft. from the basketball ring. The eyes of the basketball player are 6 ft. above the ground. 1. What is the vertical distance between the player’s line of sight and basketball ring? 2. What is the angle of elevation of the player’s line of sight when shooting a free throw to the basketball ring?
- 34. CREDITS: This presentation template was created by Slidesgo, and includes icons by Flaticon and infographics & images by Freepik Thanks GODBLESS!