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Question

In triangle ABC, CAB=40, AC = 6 cm, AB = 7 cm. The length BC is equal to_____. [sin 40=0.67, cos 40=0.76]


A

7.25 m

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B

6.55 m

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C

4.55 m

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D

5.65 m

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Solution

The correct option is C

4.55 m


Draw CDAB

In ADCsin40=CDAC0.64=CD6CD=6×0.64=3.85 mcos40=ADAC0.76=AD6AD=6×0.76AD=4.56 mFrom figure, we can see thatDB=ABADDB=74.56DB=2.44 mIn right-angled triangle CDB

BC2=BD2+DC2BC2=(2.44)2+(3.85)2BC2=5.95++17.82BC2=20.77BC=4.55 m


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