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

The correct answer is: a, sin A, R

Here we have to find the which is not uniquely determine an acute angled triangle.
By sine law in ΔABC,
we have
= = (π−A−B) = 2R
or
 =  = (A+B) = 2R
From option,
(1) If we know a, sin A, sin B, we can find b, c, and the value of angle A, B, C
(2) With a, b, c we can find ∠A, ∠B, ∠C using the cosine law.
(3) a, sin B, R are given, so sin A, b and hence sin(A+B) sin(A+B) and then C be found
(4) If we know a, sin A, R, then we can get the ratio b/sin B or c/sin(A+B) only. We cannot determine the values of b, c, sin B, sin C separately.
Therefore, the triangle cannot be determined uniquely in this case.
Therefore, the correct answer is a, sin A, R

In this question, the which is not uniquely determine an acute angled triangle. If we know a, sin A , R, then we can get the ratio b/sin B or c/sin(A+B) only. We cannot determine the values of b, c, sin B, sin C separately.