Your Practice Set – Applications and Interpretation for IBDP Mathematics
18
Paper 1 – Ambiguous Case in Sine Rule
Example
Consider the triangle ABC such that BC � 12 , AC � 9 and ABC ˆ � 28 .
( a ) Find the possible values of ˆ BAC .
( b ) If ˆ BAC is an acute angle , find AB .
[ 4 ]
[ 2 ]
Solution
( a )
( b )
sin BAC ˆ sin ABC ˆ
� ( M1 ) for sine rule BC AC
sin BAC ˆ sin 28
� ( A1 ) for substitution 12 9
ˆ 12sin 28 sin BAC �
9 BAC ˆ � 38.75283673 or 180 � 38.75283673 BAC ˆ � 38.8 or 141 A2
AB AC sin ACB ˆ � sin ABC ˆ AB 9
� sin ( 180 � 28 �38.75283673 ) sin 28
AB � 17.61405255
AB � 17.6 A1
( A1 ) for substitution
[ 4 ]
[ 2 ]
52
SE Production Limited