Which of the following pieces of data does NOT uniquely determine an acute-angled triangle `A B C(R` being the radius of the circumcircle)?

Question

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle `A B C(R` being the radius of the circumcircle)?

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle `A B C(R` being the radius of the circumcircle)?
A. `a, sin A, sin B`
B. `a, b, c`
C. `a, sin B, R`
D. `a, sin A, R`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
By sine law in `Delta ABC`, we have
`(a)/(sinA) = (b)/(sin B) = (c)/(sin (pi - A - B)) = 2R`
or `(a)/(sinA) = (b)/(sin B) = (c)/(sin (A + B)) = 2R`
(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 `angleA , angle B, angle C` using the cosine law.
(3) a, sin B, R are given, so sin A, b and hence `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