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Which of the following pieces of data do...

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 ,sinA ,sinB` (b) `a , b , c ,` `a ,sinB ,R` (d) `a ,sinA ,R`

A

a, sin A, sin B

B

a, b, c

C

a, sin B, R

D

a, sin A, R

Text Solution

Verified by Experts

The correct Answer is:
D
First solve, each option separately.
(a) If a, sin A, sin B are given, then we can determine `b=a/(sinA)sinB,c=a/(sinA)sinc.` So, all the three sides are unique.
So, option (a) is incorrect,
(b) The three sides an uniquely make an acute angled triangle, So, option (b) is incorrect.
(c ) If a, sin B, R are given, then we can determine b = 2 Rsin, Rin `A=(asinB)/(b)` So, sin C can be determine.
Hence, side c can also be uniquely determined.
(d) If a, sin A, R are given, then
`b/(sinB)=c/(sinC)=2R`
But this could not determine the exact values of b and c.
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