ࡱ> qsp|q`  bjbjqPqP %::;++++8ľX+'G@*"LLt666FFFFFFF$HhJrF+62.666FLtyoFi@i@i@6jpL(+tFi@6Fi@i@:BC, ! +Ct4 6[6nC DF0'GxC J7JCJ+C66i@66666FF?j666'G6666+++HD+++H+++  SOLUTION OF TRIANGLES 1.2 Use Sine Rule to find the unknown sides or angles of a triangle. Task 1 : Find the unknown sides of a triangle when two of its angles and one of the corresponding sides are known. (1) Diagram 1 shows the triangle ABC. Calculate the length of BC.Answer :  EMBED Equation.3   EMBED Equation.3  Using the scientific calculator, BC = 12.32 cm(2) Diagram 2 shows the triangle PQR Calculate the length of PQ. [ 8.794 cm ](3) Diagram 3 shows the triangle DEF. Calculate the length of DE.  [ 10.00 cm ](4) Diagram 4 shows the triangle KLM. Calculate the length of KM.  [ 11.26 cm ] (5) Diagram 5 shows the triangle ABC. Calculate the length of AC.Answer :  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Using the scientific calculator, AC = 11.56 cm(6) Diagram 6 shows the triangle PQR Calculate the length of PR. [ 6.527 cm ](7) Diagram 7 shows the triangle DEF. Calculate the length of EF.  [ 17.25 cm ](8) Diagram 8 shows the triangle KLM. Calculate the length of KL.  [ 16.26 cm ]Task 2 : Find the unknown sides of a triangle when two of its angles and the side not corresponding to the angles are known. (9) Diagram 9 shows the triangle ABC. Calculate the length of BC.Answer :  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Using scientific calculator, BC = 9.9996 cm or 10.00 cm(10) Diagram 10 shows the triangle ABC. Calculate the length of AC. [ 4.517 cm ](11) Diagram 11 shows the triangle PQR.  Calculate the length of PQ.  [ 3.810 cm ](12) Diagram 12 shows the triangle DEF.  Calculate the length of DE. [ 5.189 cm ] Task 3 : Find the unknown angles of a triangle when two sides and a non-included angle are given. (1) Diagram 1 shows the triangle ABC. Find (ACB.Answer :  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 (2) Diagram 2 shows the triangle KLM Find (KLM  [ 27.360 ](3) Diagram 3 shows the triangle DEF. Find (DFE.  [ 11.090 ](4) Diagram 4 shows the triangle PQR. Find (QPR.  [ 36.110 ] (5) Diagram 5 shows the triangle ABC. Find (ABC. Answer :  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 (6) Diagram 6 shows the triangle KLM. Find (KLM. [ 138.640 ](7) Diagram 7 shows the triangle DEF. Find (DFE.  [ 124.460 ](8) Diagram 8 shows the triangle PQR. Find (PQR.  [ 94.150 ]Task 4 : Find the unknown side of a triangle when two sides and a non-included angle are given. (1) Diagram 1 shows the triangle ABC. Given that (ACB is an obtuse angle, find the length of AC. Answer :  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  AC = 8.018 cm (2) Diagram 2 shows the triangle KLM Given that (KLM is an obtuse angle, find the length of ML.  [ 2.952 cm ] (3) Diagram 3 shows the triangle DEF. Given that the value of (EDF is greater than 900, find the length of DE.  [ 5.040 cm ](4) Diagram 4 shows the triangle PQR. Given that (PQR is an angle in the second quadrant of the cartesian plane, find the length of QR.  [ 2.707 cm ](5) Diagram 5 shows the triangle KLM. Given that (KLM is an angle in the second quadrant of the cartesian plane, find the length of KL. [ 9.686 cm ]     PAGE  PAGE 8 Solutions of Triangles Diagram 12  Diagram 1 5.6 cm  Diagram 2 D E F 600 350 16 15 cm Diagram 3 Diagram 4 15 cm 630 420 M K L 510 720 F E D Diagram 11 7.2 cm 280 250 Q P R  Diagram 10 Diagram 9 Diagram 5 9.2 cm 230 17.3 cm M K L Diagram 4 8.5 cm 460 6.9 cm Q P R Diagram 3 8 cm 420 11 cm F E D Diagram 2 9 cm 400 7 cm M K L 9 cm Diagram 1 14 cm 370 C A B 7.7 cm Diagram 8 12.3 cm 550 Q R P 4.4 cm Diagram 7 6.7 cm 340 F D E Diagram 6 2.8 cm 250 4.2 cm M K L 9 cm Diagram 5 14 cm 1100 C A B Diagram 4 13 cm 1300 10 cm Q P R Diagram 3 12.5 cm 430 24 3.5 cm F E D Diagram 2 15 cm 500 9 cm M K L 10 cm Diagram 1 15 cm 600 C B To find unknown angles :  EMBED Equation.3  To find unknown sides :  EMBED Equation.3  A  Diagram 5  Diagram 6 D E F 600 350 16 15 cm Diagram 7 L K M 420 630 15 cm Diagram 8 _`ij* G H [ \ ] ^ y z 3 ? @ 伱䖊ymf伱[h)h)CJaJ h?6CJjHh?CJEHU j8 h?UVmHnHujh?CJEHU ju]8 h?UVmHnHujh?CJUh?CJmHnHujh?CJUmHnHu h-CJ h>CJ h)CJ hQCJ h?CJ hwHjCJjh[TdCJUmHnHu _`         * 3 4 _ ` $If`gd-gd>         3 qkd$$Ifl0#04 la$If3 4 5 6 7 8 9 : ; < = > ? 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