Trigonometric ratios 9B 1 a d b 2 a c b

Transcription

1 Trigonometric ratios 9B 1 a a Using sin A sin B 8 sin 72 sin 30 8sin 72 sin 30 As 72 > 30, > 8 cm 15.2 cm ( ) ABC Using a 9.8 sin 27.9 sin sin 27.9 a sin cm ( ) 2 a c Using c 24 sin 22 sin110 24sin 22 c sin110 As 110 > 22, 24 cm > c cm ( ) x a Using sin A sin B y 7.5 sin 57 sin84 7.5sin 57 y sin cm ( ) ABC a Using sin A sin B a 14.7 sin 30 sin sin 30 a sin cm ( ) Using Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 1

2 2 x 25 sin 30 sin112 25sin 30 x sin112 B cm ( ) 38 Using sin B sin C y 25 sin 38 sin112 25sin 38 y sin cm ( ) e y 8 sin 50 sin 80 8sin 50 y 6.22 cm ( ) sin80 (Note: You coul use the line of symmetry to split the triangle into two right-angle 4 triangles an use cos 50. y c x a Using sin B sin A y 8 sin85 sin 35 8sin 85 y sin cm ( ) C Using x 5.9 sin 56.4 sin sin 56.4 x sin cm ( ) Using sin B sin C y 5.9 sin 72 sin sin 72 y sin cm ( ) f x Using Using x 6 sin 36.8 sin 53.2 Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 2

3 2 f 3 a 6sin 36.8 x sin 53.2 B cm ( ) 90 Using sin B sin C 6 y sin 53.2 sin 90 6sin 90 y sin cm ( ) (Note: The thir angle is 90 so you coul solve the prolem using sine or cosine; the sine rule is not necessary.) 3 c sin C sin A Using c a sin x sin sin 60 sin x ( ) 8 6sin 60 x sin x 40.5 sin C sin A Using c a sin x sin sin117 sin x sin117 x sin 9 x ( ) sin C sin B Using c sin C sin sin 28 sin C sin 28 C sin 10.8 C 22.2 x x 130 sin A sin B Using a sin x sin sin 40 sin x ( ) 11 10sin 40 x sin x a Using sin x sin Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 3

4 5.8sin sin 67.5 x sin x a sin x ( ) Angle ACB Using sin x sin sin110 sin x sin110 x sin x 48.7 e c Using sin x sin sin 80 sin x ( ) sin 80 x sin x 45.6 sin C sin B Using c sin C sin sin 55 sin C ( ) sin 55 C sin x C x ( ) Using sin x sin sin 50 sin x sin 50 x sin x 14.8 f sin B sin C Using sin B sin sin 60 sin B B x B x 77.4 () Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 4

5 5 7 a 6 q p a Using sin Q sin P PR 3 sin 45 sin 60 3 sin 45 PR 1.41 cm sin 60 ( The exact answer is 2 cm. ) r p Using sin R sin P R ( ) PQ 3 sin 75 sin 60 3 sin 75 PQ 1.93 cm sin 60 Using sin x sin sin 75 sin x sin 75 x sin x 43.2 So ABC Using sin B sin C y 5.5 sin 61.8 sin sin 61.8 y sin 75 y 5.02 sin P sin R Using p r sin P sin sin 75 sin P ( ) 15 12sin 75 P sin Angle QPR 50.6 Angle PQR Using sin A sin sin 45 sin A sin 45 A sin x A x 101 Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 5

6 7 Using sin B sin C y 10.8 sin x sin sin x y sin 45 y 15.0 c 1 5sin102 x sin x 54.6 In triangle ABC: BAC x 13.4 So ADB a Using in ABD sin D sin A y 6 sin156.6 sin13.4 6sin156.6 y sin x In ABC, cos 20 7 x 7cos sin D sin A Using in ADC a sin y sin100 x 12.2 xsin100 sin y 12.2 xsin100 y sin y 32.1 e sin C sin A Using in ABC c a sin x sin x 21.8 ( ) a Using in ABD sin A sin D y 6.4 sin 24 sin sin 24 y sin120 y In triangle BDC: C sin B sin C Using sin x sin sin102 sin x 6 f (The aove approach fins the two values inepenently. You coul fin y first an then use it to fin x, ut if your answer for y is wrong then x will e wrong as well.) Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 6

7 7 f 8 sin D sin B Using in BDC sin x sin sin 80 sin x sin 80 x sin x 45.9 In triangle ABC: ACB x Using sin A sin sin sin A sin A sin So y y 3.87 ( ) 8 Using BC 6 sin 35 sin 65 6sin 35 BC 3.80 km sin 65 9 a In triangle ABD: DAB 43 isosceles ( 43 ) So ADB As the triangle is isosceles you coul work with right-angle triangles, ut using the sine rule a sin D sin A AB 5 sin 94 sin 43 5sin 94 AB 7.31cm ( ) sin 43 BAC ABC (Alternate angles an angles on a straight line.) ACB a Using sin B sin C AC 6 sin80 sin 65 6sin 80 AC 6.52 km sin 65 In triangle ADC: ADC So CAD Using CD 5 sin 22 sin 72 5sin 22 CD 1.97 cm sin a In triangle ABD: sin B sin A a sin B sin sin 66 So sin B 136 B Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 7

8 10 a So the angle etween AB an BD is Using triangle BCD: sin B sin C sin B sin sin 98 So sin B 136 B So the angle etween BC an BD is The angle etween the fences AB an BC is In triangle ABD: Angle ADB Using the cosine rule: a + 2acos D cos So So the length of the fence AB is 148 m (). 11 Multiply top an ottom y 2 1: x 4( 2) ( 2 1)( 2+ 1) 4( 2) a Using the left-han triangle, the angles are 40, 128 an 12. ( an 180 ( ) 12 ) a sin A sin B a 15 sin128 sin12 15sin128 a sin12 a Using the larger right-angle triangle: height sin Height sin The height of the uiling is 36.5 m (). Assume that the angles of elevation have een measure from groun level. Using 4 x x sin y sin 30 4 x sin 30 xsin y 1 1 ( 4 x) x 2 2 Multiply throughout y 2: 4 x x 2 x+ 2x 4 x x Pearson Eucation Lt Copying permitte for purchasing institution only. This material is not copyright free. 8