O-LevelMathematicsTrigonometry4024/21 · Oct/Nov 2014 · Q511 Marks

In triangle ABC, AC = 14cm, BC = 8cm and ACB = 122°.

(a)Show that AB = 19.5cm, correct to 3 significant figures.[4]
(b)Calculate ABC.[3]
(c)A rhombus, BDEC, of area 52 cm² and sides 8 cm is placed next to triangle ABC as S diagram. Given that BCE is an obtuse angle, calculate the reflex angle ACE.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

[4] 19.46 seen
[4] Working seen. No wrong working.
[4] M2 for 14² +8² - 2×14×8 × cos 122
[4] and A1 for 378.7 soi
[4] or M1 for an incorrect formula with one error and A1 for 141.3 or 319.35 or 250.7 soi
[3] 37.5 to 37.6
[3] M2 for 14 sin122 / 19.5
[3] or M1 for sin B / 14 = sin 122 / 19.5 oe
[3] SC1 for correct method for wrong angle
[4] 247 to 248
[4] M1 for 0.5 × 8 × 8 × sinC = 26 oe soi
[4] and A1 for 54.34
[4] and M1 for 180 – their 54.34 or 238 - their 54.34
[4] SC1 after 0 for CE = 8

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