I.G.C.S.E. Sine and Cosine Rules. You can access the solutions from the end of each question

Transcription

1 I.G..S.E. Sine nd osine Rules Index: Plese lik on the question numer you wnt Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 You n ess the solutions from the end of eh question

2 Question 1 For eh of the following find eh side mrked with the letter m 6 m m lik here to red the solution to this question lik here to return to the index

3 Solution to question m 23 sin sin sin Using we hve sin sin sin23 6 sin35 6sin m sin sin m sin sin sin122 sin35 sin m 7.1 m 56 Here we hve two sides nd the inluded ngle so we hve to use the osine rule. + 2os ( 5.6)( 7.1) os m lik here to red the question gin lik here to return to the index

4 Question 2 In eh of the following tringles find the missing ngles m 9.8 m 4.5 m 7.6 m m lik here to red the solution to this question lik here to return to the index

5 Solution to question m m sin sin sin Using sin sin we hve sin sin84 4.2sin84 sin sin84 sin Here we hve three sides nd we re required to find n ngle, so we use the osine rule. 4.5 m 5.7 m 7.6 m + os ( )( ) ( 6)( 5. 7) 1 os os ( )( ) ( 5)( 5. 7) 1 os lik here to red the question gin lik here to return to the index

6 Question 3 destroyer D nd frigte F leve port P t the sme time. The digrm shows the destroyer, siling 45 km on ering of 050 nd the frigte siling 35 km on ering of 165. How fr re the ships prt? D W E km S P km F lik here to red the solution to this question lik here to return to the index

7 Solution to question 3 D 45 km W E 50 S P km P f 45 km km d F p D F We hve to lulte DF. Drwing tringle PDF, we hve ˆ P Using the osine rule s we hve two sides nd the inluded ngle. p d + f df osp ( )( ) os p km lik here to red the question gin lik here to return to the index

8 Question 4 Find ll the ngles of tringle whose sides re in the rtio 4 : 5 : 6. lik here to red the solution to this question lik here to return to the index

9 Solution to question 4 First drw digrm nd lel the sides ow lulting ngle  nd ˆ using the osine rule, we hve os ˆ ( )( 5) ˆ 1 1 os os ˆ ( )( 5) ˆ 1 3 os ow using tht the ngle sum of tringle is 180, we hve ˆ lik here to red the question gin lik here to return to the index

10 Question 5 From lighthouse L n oil tnker is 12 km wy on ering of 126 nd r ferry is 15 km wy on ering of 210. Drw digrm lerly showing L, nd. Find. the distne etween nd. the ering of from lik here to red the solution to this question lik here to return to the index

11 Solution to question 5 First drwing digrm L km km ow drwing tringle L. ote tht ˆ L km L km l. The distne etween the two ships is given y l. Using the osine rule l + 2 osl ( 15)( 12) os l km lik here to ontinue with the question or go to next pge

12 . 15 km θ L km α β The required ering is α + β s shown in the ove digrm. θ α (llied ngles). onsidering tringle L in prt 15 km L km β l km + l Using the osine rule os β os 2l ( 15)( ) os 2( 15)( ) The required ngle is α + β The ering of from is 071. lik here to red the question gin lik here to return to the index

13 Question 6 n irliner flies from Hethwik irport H, 400 km on ering of 135 to nd then 500 km on ering of 260 to, nd then returns to the irport t H.. Drw digrm, showing lerly H, nd.. lulte the length nd ering of the return journey from to H. lik here to red the solution to this question lik here to return to the index

14 Solution to question 6. First drw digrm. H km km. H km α β 260 h 500 km From the digrm α therefore β We re required to find H Using the osine rule we hve + h 2hos ( )( ) os km lik here to ontinue with the question or go to next pge

15 θ 135 H 400 km α h 500 km Using osine rule osh H + h ( )( ) os 74.5 ( )( ) The ering of H from is given y α ow θ nd hene α The ering of H from is lik here to red the question gin lik here to return to the index