حل السؤال 25، 4MA1/1HR يونيو 2023: الاختيار بين قانوني الجيب وجيب التمام

1. 1Area of triangle = ½ × AB × AC × sin A
2. 2½ × (2x − 1)(2x + 1) × sin 30° = x² + x − 3.75
3. 3(2x − 1)(2x + 1) = 4x² − 1 and sin 30° = 0.5
4. 40.25 × (4x² − 1) = x² + x − 3.75
5. 5x² − 0.25 = x² + x − 3.75
6. 6−0.25 = x − 3.75
7. 7x = 3.75 − 0.25 = 3.5
8. 8AB = 2 × 3.5 − 1 = 6 cm and AC = 2 × 3.5 + 1 = 8 cm, with angle A = 30°
9. 9BC² = 6² + 8² − 2 × 6 × 8 × cos 30°
10. 10BC² = 100 − 83.14 = 16.86
11. 11BC = √16.86 = 4.106 cm
12. 12AC = 8 cm is the longest side, so the largest angle is ABC, the angle opposite it
13. 13cos ABC = (6² + 4.106² − 8²) ÷ (2 × 6 × 4.106)
14. 14cos ABC = (36 + 16.86 − 64) ÷ 49.28 = −11.14 ÷ 49.28 = −0.226
15. 15ABC = 103.06°
16. 16The largest angle is 103°

Answer103