Solving Right Triangle Grade 9 Quarter 4.pptx

Solving Right Triangle Grade 9 Quarter 4.pptx

1. Trigonometric Functions

2. Solve a right triangle given an angle and a side or two sides. Solve problems involving angles of elevation and depression.

3. TO Solve a tr ia ngle means to find all of the missing measures of the angles and sides. There are two types of problems: right triangles with a side and an angle or two sides We will use the trig ratios to find the missing pieces. The key is to match the information we have and need to find with a corresponding trig ratio.

4. Example: Solve right triangle ABC, i f A = 3 4 o 30 ’ and c = 12.7 i n. c = 12.7 i n.

5. Example: Solve right triangle ABC, if A = 34 o 30’ and c = 12.7 i n. The easiest part is to calculate B by subtracting A from 90°. B = 90 - 34 o 30’ = 55° 30’

6. Example: Solve right triangle ABC, if A = 34 o 30’ and c = 12.7 i n. To find the missing sides, since we have the hypotenuse, we will use sine and cosine. sin

7. Example: Solve right triangle ABC, if A = 34 o 30’ and c = 12.7 i n. B To find the missing sides, since we have the hypotenuse, we will use sine and cosine. sin A sin34°30’ = a 12.7 A c = 12,7 in. b

8. 12 16 Find the missing parts given two sides. C R A

9. Example: Solve right triangle ABC, iI A — — 34° 30' and c — — 12.7 in. B To find the missing sides, since we have the hypotenuse, we will use sine and cosine. sin A — — — sin34°30' = 12.7 34° 30’ a = 12.7sin 34°30' = 7.19 in

10. Example: Solve fight triangle ABC, ifA - — 34° 30' and c = 12.7 in. B To find the missing sides, since we have the hypotenuse, we will use sine and cosine. b cos A — — — cos34°30’ = b 12.7 A c = 12,7 in. b

11. Example: Solve right triangle ABC, iI A — — 34° 30' and c — — 12.7 in. B b To find the missing sides, since we have the hypotenuse, we will use sine and cosine. cos A — — — cos34°30’ = b 1Z.7 34° 30’ b - - 1 2.7cos34°30’ = 10.5 in

12. Example: Solve right triangle ABC, iI a — — 29.43 cm and c — — 53.58 cm This time, we'll find the missing side first, using the Pythagorean Theorem. 53.58" — 29.43" = 44.77 cm

13. Example: Solve right triangle ABC, iI a — — 29.43 cm and c — — 53.58 cm We can find fi by using the inverse of the sine function because we have n and c. sin fi = —

14. Example: Solve fight triangle ABC, if o = 29.43 cm and r = 53.58 cm We can find A by using the inverse of the sine function because we have n and c. B sink —— — A — — sin*' 29.43 53.58 b

15. Example: Solve right triangle ABC, iI a — — 29.43 cm and c — — 53.58 cm We can find fi by using the inverse of the sine function because we have n and c. B sin fi = — A — — sin A — — 33.32° 29.43 53.58 r = 53.S8 cm b

16. Example: Solve right triangle ABC, iI a — — 29.43 cm and c — — 53.58 cm We can find fi by using the inverse of the sine function because we have n and c. B sin fi = — A — — sin A — — 33.32° 29.43 53.58 r = 53.S8 cm b B — — 90 — 33.32 = 56.68°

17. An angle of elevation is an angle formed by a horizontal line and the line of sight to a point above the line. An anpfe of depression is formed by a horizontal line and a line of sight to a point below the line. Angle of depression To identify w\ ethe a« angle is an angle of elevation or depression, check whether the line of sight is gj2i2_yv or elm the horizontal line.

18. Example: If a tree casts a shadow 18 feet long when the sun is at an elevation of 35', how tall is the tree to the nearest foot?

19. Example: If a tree casts a shadow 18 feet long when the sun is at an elevation of 35', how tall is the tree to the nearest foot? Step 1: Draw a sketch and label it. 18’ (adj)

20. Example: If a tree casts a shadow 18 feet long when the sun is at an elevation of 35', how tall is the tree to the nearest foot? Step 1: Draw a sketch and label it. 18’ (adj) Step 2: use the sketch to set up an equation. 18

21. set up an equation. Step 3: Solve the equation. Example: If a tree casts a shadow 18 feet long when the sun is at an elevation of 35', how tall is the tree to the nearest foot? Step 1: Draw a sketch and label it. 18’ (adj) Step 2: use the sketch to 18 x — — 18tan35” x — — 13 feet

22. Example: A plane, at an altitude of 3000 feet, observes the airport at an angle of 27°. What is the horizontal distance between the plane and the airport to the nearest foot?

23. Example: A plane, at an altitude of 3000 feet, observes the airport at an angle of 27°. What is the horizontal distance between the plane and the airport to the nearest foot? 3000'

24. Example: A plane, at an altitude of 3000 feet, observes the airport at an angle of 27°. What is the horizontal distance between the plane and the airport to the nearest foot? (27°) 3000'

25. Example: A plane, at an altitude of 3000 feet, observes the airport at an angle of 27°. What is the horizontal distance between the plane and the airport to the nearest foot? 27° 3 D 0’ (°° tan 27° 3000 (27 ) (adj) 3000 tan 27° = 5888 feet

26. College Algebra Page 538: 6- 12, page 513: 54- 62, page 501: 74- 86 (all evens)