Trigonometric EquationMedium
Question
There exists a triangle ABC satisfying the conditions
Options
A.b sin A = a , A < 
B.b sin A > a, A >
C.b sin A > a, A <
D.b sin A < a, A < , b > a
, b > aSolution
The sine formula is 
⇒ a sin B = b sin A
(a) : b sin A = a ⇒ a sin B = a ⇒ B =
Since, ∠A < therefore, the triangle is possible.
(b) and (c) : bsin A > = a ⇒ asin B > a ⇒ sin B > 1
∴ ᐃ ABC is not possible.
(d) : bsin A < a ⇒ asin B < a
⇒ sin B < 1 ⇒ ∠B exists
Now, b > a ⇒ B > A since A <
∴ The triamgle is possible.
⇒ a sin B = b sin A (a) : b sin A = a ⇒ a sin B = a ⇒ B =
Since, ∠A <
therefore, the triangle is possible. (b) and (c) : bsin A > = a ⇒ asin B > a ⇒ sin B > 1
∴ ᐃ ABC is not possible.
(d) : bsin A < a ⇒ asin B < a
⇒ sin B < 1 ⇒ ∠B exists
Now, b > a ⇒ B > A since A <
∴ The triamgle is possible.
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