Maths-

General

Easy

Question

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

- a, sin A, sin B
- a, b, c
- a, sin B, R
- a, sin A, R

Hint:

### Here we have to find the following data does not uniquely determine an acute angled triangle ABC. And also, R being the radius of the circumcircle. Here uses the sine law to find the solution.

## 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.

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