Question

Can someone please help me!?
In ΔABC, a = 7.2cm, b = 9.3cm, ∠A = 35° (6)
a. Determine the number of possible solutions.
b. Determine the measure of ∠B if it exists.

Answer 1

i) Applying sine law of triangles, b/sin(<B) = a/sin(<A)

==> 9.3/sin(B) = 7.2/sin(35°)

ii) Solving the above, sin(B) = 0.7409

This give <B = 47°48'; as well sin(180 - B) = sin(B);
So another value for <B = 180° - 47°48' = 132°12'

Thus <B = Either 47°48' or 132°12'
Both values of <B are possible.

Answer 2

i) Applying sine law of triangles, b/sin(<B) = a/sin(<A)

==> 9.3/sin(B) = 7.2/sin(35°)

ii) Solving the above, sin(B) = 0.7409

This give <B = 47°48'; as well sin(180 - B) = sin(B);
So another value for <B = 180° - 47°48' = 132°12'

Thus <B = Either 47°48' or 132°12'
Both values of <B are possible.