SPM 2021 Add Maths Trial Paper (Selangor) – Paper 1 (Question 15)


Question 15:
Diagram 6 shows a triangle ABC. Given that the area of triangle ABC is 21 cm2 and ∠BAC is obtuse angle.
Diagram 6

Find
(a) ∠BAC, [3 marks]
(b) the length of BC, in cm, [2 marks]
(c) the length of the perpendicular line from A to BC. [3 marks]


Solution:
(a)

Area of Δ= 1 2 absinC 21= 1 2 ( 14 )( 5 )sinBAC sinBAC= 21×2 14×5 sinBAC=0.6 BAC= 36.87 o Obtuse angle of BAC= 180 o 36.87 o = 143.13 o


(b)

B C 2 = 14 2 + 5 2 2( 14 )( 5 )cos 143.13 o B C 2 =221( 112 ) BC= 333      =18.248 cm


(c)

Given that the area of Δ ABC=21  cm 2 Perpendicular line from A to BC is the verticle height, h of the , 1 2 ×h×18.248=21 h= 21×2 18.248   =2.302 cm


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