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Question

In triangle ABC, B= 30, C=45. If CD = 8 cm, then AB is equal to


A

8 cm

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B

16 cm

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C

83 cm

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D

163 cm

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Solution

The correct option is B

16 cm


In ΔADC, ACD=45,DAC=180(90+45)=45

Therefore, angles of ADC are 45,45,90

sin(45):sin(45):sin(90)

12:12:1

1:1:2

Therefore, the corresponding sides will be in the ratio 1:1:2

4545901:1:2ADDCAC8 cm8 cm82 cm

AD = 8 cm

Now, in triangle ABD A= (1809030)= 60.

Therefore, angles of triangle ABD are 30,60,90

Hence, the corresponding sides will be in the ratio 1:3:2

3060901:3:2ADBDAB8 cm83 cm16 cm

Hence, AB =16 cm


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