Question

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle ABC (R being the radius of the circum-circle)

• A. $a , \sin A , \sin B$
• B. $a , b , c$
• C. $a , \sin B , R$
• D. $a , \sin A , R$

Answer 1

Answer: (D)

$a , \sin A , R$

Answer 2

$\frac { a } { \sin A } = R$ and $b = 2 R \sin B$ . So two sides and two angles are known. So $\Delta$ is uniquely known in case (1).

If a, b, c are known the $\Delta$ is uniquely known in case (2). $b = 2 R \sin B , \sin A = \frac { a } { 2 R }$ So, sides a, b and angle A, B are known. So $\Delta$ is uniquely known in case (3).

$\frac { a } { \sin A } = R$ So, only a side and an angle is known. So, $\Delta$ is not uniquely known in case (4).