O-LevelMathematicsTrigonometry4024/22 · Oct/Nov 2020 · Q911 Marks
(a) [Figure 9.1] In triangle ABC, AC = 6.4cm, BC = 9.5cm and BÂC = 79°.
- (a)(i)Calculate ABC .[3]
- (a)(ii)Calculate the area of triangle ABC.[3]
- (b)(i)Calculate BDC.[3]
- (b)(ii)Calculate the angle of elevation of D from C.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [3] M1 for sine rule setup: 6.4 / sin(ABC) = 9.5 / sin 79 oe; M2 for sin(ABC) = (6.4 sin 79) / 9.5; Final answer 41.4[0] or 41.39...°.
- [3] Dep on 3 marks in (a)(i) or 41.4[0] used; M1FT for angle C = 180 - 79 - their 41.4; M1 for 1/2 * 6.4 * 9.5 * sin(their C) oe; Final answer 26.2[2...] cm².
- [3] M1 for cosine rule setup for angle BDC (9.5² = 9.8² + 8.2² - 2 × 9.8 × 8.2 × cos(BDC)); M2 for cos(BDC) = (9.8² + 8.2² - 9.5²) / (2 × 9.8 × 8.2); Final answer 63[.0] or 62.97...°.
- [2] M1 for cos(angle_elevation) = 6.4 / 8.2 (or equivalent trig for triangle ADC, finding vertical height of D from A); Final answer 38.7 or 38.69...°.
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