Answer:
A. a = 16.23 and b = 17.99
Step-by-step explanation:
The addition of the three angles of the triangle is equal to 180°. So,
C + 64° + 85° = 180°
C = 180° - 64° - 85°
C = 31°
The law of sine states:
sin(A)/a = sin(B)/b = sin(C)/c
where c is the side opposite to angle C
Taking angles A and C, and sides a and c, we get
sin(A)/a = sin(C)/c
sin(64°)/a = sin(31°)/9.3
sin(64°)*9.3/sin(31°) = a
a = 16.23
Taking angles B and C, and sides b and c, we get
sin(B)/b = sin(C)/c
sin(85°)/b = sin(31°)/9.3
sin(85°)*9.3/sin(31°) = b
b = 17.99
