Trigonometric EquationHard
Question
Which of the following pieces of data does not uniquely determine an acute- angled triangle ABC (R being the radius of the circumcircle) ?
Options
A.a, sin A, sin B
B.a, sin A, sin B
C.a, sin B, R
D.a, sin A, R
Solution
Here, for
(a) If a, sin A, sin B are given, then we can determine
sin B, c = sin C So, all the three sides are unique.
So, option (a) is incorrect.
(b) The three sides can uniquely make an acute angled triangle, So, option (b) is incorrect.
(c) If a, sin B, R are fiven, then we can determine B = 2Rsin B, sin A =
. So C can be determinedHence, side c can also be uniquely determined.
(d) If a, sin A, R are given, then
= 2C
But this could not determine the exact values of b and c.
(a) If a, sin A, sin B are given, then we can determine
sin B, c = sin C So, all the three sides are unique.So, option (a) is incorrect.
(b) The three sides can uniquely make an acute angled triangle, So, option (b) is incorrect.
(c) If a, sin B, R are fiven, then we can determine B = 2Rsin B, sin A =
. So C can be determinedHence, side c can also be uniquely determined. (d) If a, sin A, R are given, then
= 2CBut this could not determine the exact values of b and c.
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