Help with this question. pls

for triangle ABC suppose you are given the measure of angle A and the lengths of sides a and c. under which of the following conditions would there be two possible solutions?
a) c > a > c sin A
b) a > c or a < b
c) a < c sin A
d) a = c sin A

Hello

The answer is a

c > a > c sin A

Look at this :

http://img507.imageshack.us/img507/7264/…
BD is perpendicular to side b
E, D, F are on side c
To be clear, E and F are possible positions of C

You see that there will be two possible solutions ( a and a') if E is between A and D
That means BD < a < c

Sin A = BD/c ==> BD = c sin A

Then c sin A < a < c

Hope it helps

Bye !