Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
To find unknown sides : To find unknown angles : a b c sin A sin B sin C sin A sin B sin C a b c 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. Answer : BC 8.2 0 sin 75 sin 400 BC Diagram 1 8.2 sin 750 sin 40 0 Using the scientific calculator, BC = 12.32 cm Calculate the length of BC. (2) Diagram 2 shows the triangle PQR Diagram 2 [ 8.794 cm ] Calculate the length of PQ. (3) Diagram 3 shows the triangle DEF. D 15 cm 600 E 350 16’ Diagram 3 F Calculate the length of DE. [ 10.00 cm ] (4) Diagram 4 shows the triangle KLM. L K 420 0 63 15 cm Diagram 4 M Calculate the length of KM. [ 11.26 cm ] Solutions of Triangles 1 (5) Diagram 5 shows the triangle ABC. Answer : ABC 180 0 40 0 75 0 65 0 AC 8.2 0 sin 65 sin 40 0 BC Diagram 5 8.2 sin 65 0 0 sin 40 Using the scientific calculator, Calculate the length of AC. AC = 11.56 cm (6) Diagram 6 shows the triangle PQR Diagram 6 Calculate the length of PR. [ 6.527 cm ] (7) Diagram 7 shows the triangle DEF. D 15 cm 600 E 350 16’ Diagram 7 F Calculate the length of EF. [ 17.25 cm ] (8) Diagram 8 shows the triangle KLM. L K 420 0 63 15 cm Diagram 8 M Calculate the length of KL. [ 16.26 cm ] Solutions of Triangles 2 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. Answer : ABC 1800 470 780 550 BC 11.2 0 sin 47 sin 550 BC 11.2 sin 47 0 0 sin 55 Diagram 9 Using scientific calculator, Calculate the length of BC. BC = 9.9996 cm or 10.00 cm (10) Diagram 10 shows the triangle ABC. Diagram 10 Calculate the length of AC. [ 4.517 cm ] (11) Diagram 11 shows the triangle PQR. 7.2 cm P 250 0 28 R Diagram 11 Q Calculate the length of PQ. [ 3.810 cm ] (12) Diagram 12 shows the triangle DEF. D 720 E 510 5.6 cm F Diagram 12 Calculate the length of DE. [ 5.189 cm ] Solutions of Triangles 3 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. Answer : A 10 cm sin C sin 60 0 10 15 15 cm 600 B sin C C Diagram 1 10 sin 60 0 15 sin C 0.5774 C sin 1 0.5774 C 35.27 0 Find ACB. (2) Diagram 2 shows the triangle KLM 15 cm L K 9 cm 500 Diagram 2 M Find KLM [ 27.360 ] (3) Diagram 3 shows the triangle DEF. D 3.5 cm 12.5 cm 430 24’ E F Diagram 3 Find DFE. [ 11.090 ] (4) Diagram 4 shows the triangle PQR. 13 cm R P 10 cm 0 130 Diagram 4 Q Find QPR. [ 36.110 ] Solutions of Triangles 4 (5) Diagram 5 shows the triangle ABC. Answer : sin A sin 110 0 9 14 9 sin 1100 sin A 14 A 14 cm 1100 Diagram 5 B sin A 0.6041 A sin 1 0.6041 A 37.160 9 cm C Find ABC. ABC 180 0 110 0 37.16 0 32.84 0 (6) Diagram 6 shows the triangle KLM. 4.2 cm K L 2.8 cm 250 Diagram 6 M Find KLM. [ 138.640 ] (7) Diagram 7 shows the triangle DEF. E D 340 4.4 cm 6.7 cm F Diagram 7 Find DFE. [ 124.460 ] (8) Diagram 8 shows the triangle PQR. P 12.3 cm R 550 7.7 cm Q Diagram 8 Find PQR. [ 94.150 ] Solutions of Triangles 5 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. Answer : sin C sin 37 0 14 9 14 sin 37 0 sin C 9 A 370 14 cm B Diagram 1 C sin C 0.9362 9 cm C sin 1 0.9362 Given that ACB is an obtuse angle, find the length of AC. C 110.580 B 1800 110.580 370 32.420 AC sin 32.42 0 AC 9 sin 37 0 9 sin 32.42 0 sin 37 0 AC = 8.018 cm (2) Diagram 2 shows the triangle KLM 9 cm L K 0 40 7 cm M Diagram 2 Given that KLM is an obtuse angle, find the length of ML. [ 2.952 cm ] Solutions of Triangles 6 (3) Diagram 3 shows the triangle DEF. D 8 cm 420 E 11 cm F Diagram 3 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. 8.5 cm P R 460 6.9 cm Diagram 4 Q 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. K L 0 23 17.3 cm 9.2 cm Diagram 5 M Given that KLM is an angle in the second quadrant of the cartesian plane, find the length of KL. [ 9.686 cm ] Solutions of Triangles 7 Solutions of Triangles 8