N33. Trigonometry Preview Assignment. Part 1: Right Triangles. x = FMP1O NAME:

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1 x= 4. Trigonometry Preview ssignment FMP1O NME: B) Label all the sides of each right triangle (Hypotenuse, djacent, Opposite) N33 ) Find the measure of each unknown angle (variable) in the triangle. Remember that all = 5. angles in a triangle add up to Part 1: Right Triangles x = I

2 Part 2: Pythagorus ) Label the triangles (legs are a & b, hypotenuse is c). B) Use Pythagorean relation to solve for the missing side length. (c2 = a2 + b2) or (a2 = c2. b2) or (b2 c2 a2) $

3 FMPIO Lesson 1: Unit 3: Trigonometry Primary Trig Ratios (Finding Lengths) Trigonometry is the study of triangles. For the right triangles below measure all the side lengths and all the angles. Without measuring find the missing side lengths on the triangle below. 4 cm x y

4 b) cos75 Find then exp ain the resu t. hypotenus hypotenus adjacent adjacent tan L = opposite SOH H TO djacent Opposite Three Primary Trigonometric Ratios c) tan65 a) sin3o Example 1: sin Z = oppostie cos L =

5 Example 2: Use the sine, cosine or tangent ratios to find x andy. a) b) y 62 x c) 2Zi x HW: 1) Pg 82: 3-5,9 2) Pg 101:3-5,12

6 To find angles we use the inverse trig ratios sin Example 1: alculate sin, cos, tan, sin, cos, tan hypotenus hypotenus adjacent sinz= cosl4= tanl4= oppostie adjacent opposite SOH H TO djacent Opposite Three Primary Trigonometric Ratios Lesson 2: Finding ngles Unit 3: Trigonometry FMPIO ratio of sides and give the corresponding angle). inverse trig ratios do the opposite operation of sine, cosine and tangent (they take the any 1, cos 1,tan 1. These are often written or For any angle sine, cosine and tangent give the corresponding ratio of sides in a right triangle. Inverse Trig Ratios called arcsine, arccosine or arctangent to avoid confusion with reciprocals. The

7 Example 2: a) For the triangle below find tan L and L. 11 b) For the triangle below find cos L and L. ) For the triangle below find sin L and L. J Example 3: Find all missing angles. 16cm HW: 1) Pg. 75:3-5,8 2) Pg. 95: 4-8,10

8 ratio of sides and give the corresponding angle). inverse trig ratios do the opposite operation of sine, cosine and tangent (they take the any 1,tan 1. These are often written or triangle. Example 1: alculate sin, cos, tan, sin, cos, tan SOH H TO djacent Opposite Three Primary Trigonometric Ratios Lesson 2: Finding ngles Inverse Trig Ratios Unit 3: Trigonometry sinz= cosl= tan Z= FMPIO For any angle sine, cosine and tangent give the corresponding ratio of sides in a right called arcsine, arccosine or arctangent to avoid confusion with reciprocals. The To find angles we use the inverse trig ratios sin-, cos 4 B hypotenus hypotenus adjacent opposite adjacent opposite

9 Example 2: a) For the triangle below find tan L and Z. 11 b) For the triangle below find cos L and L. ) For the triangle below find sin L and L. Example 3: Find all missing angles. 16cm HW: 1) Pg. 75:3-5,8 2) Pg. 95: 4-8,10

10 FMPIO Unit 3: Trigonometry Lesson 3: Solving Right Triangles Solving a Triangle Solving a right triangle means finding all missing lengths and angles. When solving a right triangle try to use only the original numbers to find each missing value. The ngle sum of a Triangle = 1800 Pythagoras Theorem: c2 =a 2 2 +b Example 1: Solve the following triangles: a) 16cm 25cm B

11 b) Given that ang e = in B c) K 23.0 cm J 9.0 cm L HW: Pg. 82: 3-5,9 Pg. 101:3-5 Pg.111:3-6

12 /1 nale of Inclination (Elevation): upward angle from the horizontal Lesson 4: Trig Word Problems Unit 3: Trigonometry FMPIO wall? ngle of Declination (Depression): downward angle from the horizontal the foot of the flag pole. What is the angle of inclination of the guy wire? the wall What angle, to the nearest degree, does the ladder make with the Example 1: guy wire for a flag pole is 10 m long. The foot of the guy wire is 7 m to Example 2: 10-ft ladder leans against the side of a building with its base 4-ft from \ngie of Depresson [tori,ntaf Iiorinta / Pnç$ect&evatiai

13 elevation to the top of the building to be 37. The transit is set at a height Example 4: surveyor, 31 m from a building, uses a transit to measure the angle of Example 3: The angle of elevation of the sun is 68 when the tree casts a shadow 14.3 m long. How tall is the tree? of 1.5 m. a) alculate the distance from the transit to the top of the building. b) alculate the height of the building. HW: 1) Pg 76: 12,14, ) Pg 82: 6-8 3) Pg 96: ) Pg 101: 6,7,9

14 FMPIO Unit 3: Trigonometry Lesson 5: Problems Involving More than One Right Triangle Example 1: alculate the length of x. a) 8 cm x b) 12cm x

15 cm a) 8 cm b) B B Example 2: acu late the measure of angle B 5 cm 6 cm 5 cm

16 Example 3: Two TV towers are 40.5 m apart. From the top of shorter tower the angle of elevauon to the top of the taller tower is The angle of depression to the base of the taller tower is a culate the height of each tower. HW: Pg 118: 3(a,c), 4(a,c), 6,8,9,14

17 Unit 3: Trigonometry Review Name: nearest metre. 1. Find tanl4 11 B.± 11 D What is the measure L? B. 38 B D What is the measure of Lx to the nearest degree? D B. 13 B D window on the fourth floor of a building is 20 m above the ground. From the window, the angle of depression to the base of a nearby building is 31 and the angle of elevation to the top of the building is 40. How tall is the nearby building to the B. 48 D.72

18 5. Determine tan and tan B a. tan = 1.25; tan = 0.8 b.tan = 0.8; tan = c.tan = 0.8; tan = 1.25 d.tan = ; tan = Determine the angle of inclination of the line to the nearest tenth of a degree. a b c d Determine the measure of angle BD to the nearest tenth of a degree. D 8cm 19cm B a b c d. 24.9

19 4Jc Determine the tangent ratio for angle K. L M c.sin=0.6; cos=1.3 d.sin=0.6; cos= a b. 37 K 37 c d Determine the length of side z to the nearest tenth of a centimetre. a. 9.7 cm b. 2.6 cm c. 5.4 cm d. 8.5 cm 10. Determine sin and cos to the nearest tenth B a. sin= 1.7; cos=0.8 b. sin = 0.8; cos = 0.6

20 11. Determine the measure of angle D to the nearest tenth of a degree. D E F a b c d Determine the measure of angle Q to the nearest tenth of a degree. P 7 Q R a b c d helicopter is hovering 200 m above a road. car stopped on the side of the road is 300 m from the helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree? a. 56 b. 48 c. 42 d rope that anchors a hot air balloon to the ground is 136 m long. The balloon is 72 m above the ground. What is the angle of inclination of the rope to the nearest tenth of a degree? a b.62.1 c.32.0 d. 27.9

21 15. Two guy wires are attached to the top of a radio tower. The wires are 75 ft. and 52 ft. long. The longer wire is anchored to the ground at a point 58 ft. from the base of the tower. The shorter wire is anchored to the ground at a point between the base of the tower and the longer wire. alculate the angle of inclination of the shorter guy wire to the nearest tenth of a degree. a b c d Determine the perimeter of an equilateral triangle with height 11.9 cm. Give the measure to the nearest tenth of a centimetre. a cm b cm c cm d cm 17. Determine the Oength of RS to the nearest tenth of a centimetre. R Q S a. 6.7cm b. 9.3 cm c cm d. 3.3 cm T 18. Two trees are 55 yd. apart. From a point halfway between the trees, the angles of elevation of the tops of the trees are measured. What is the height of each tree to the nearest yard? tree tree 1/ 55 yd. a. 33 yd.; 31 yd. b. 19 yd.; 15 yd. c. 41 yd.; 50 yd. d. 40 yd.; 49 yd.

22 B [ a.211ft. b.112ft. c.129ft. d.276ft. 19. From the top of an 80-ft. building, the angle of elevation of the top of a taller building is 49 and the angle of depression of the base of this building is 62. Determine the height of the taller building to the nearest foot. 20. alculate the measure of angle B to the nearest tenth of a degree. 7 cm D 4 cm a b c d Determine the length of to the nearest tenth of a centimetre. B 38.9 cm 43.3 cm D a. 70.4cm b cm c cm d. 41.9cm

23 diagram below. (this is a very nasty question...) alculate the length of the shadow cast by a building 40m high. 2. t a certain time of day, the rays of the sun strike the ground at an angle of 25. Written Responses \ \ ---p / horizontal 22. From the top of a cliff 60 m above a river, angles are measured as shown in the 1. From the top of a lighthouse, 40m above the sea, the angle of depression to a boat is 200. How far is the boat from the base of the lighthouse?. 45 m B. 53 m. 62 m D. 71 m alculate the width, w, of the river. (nswer to the nearest metre.) 60

24 3. From a point 14.5m from the base of a flagpole, the angle of elevation to the top of the flagpole is I 5. If the person making the observations is I.5m tall, how high is the flagpole?