Question

Solve triangle ABC

c = 10, B = 35°, C = 65°

Question options: A = 80°, a = 10, b = 6.3

A = 80°, a = 6.3, b = 10.9

A = 80°, a = 10.9, b = 6.3

A = 80°, a = 73.6, b = 6.3

Answer 1

That figure obviously doesn't go with this problem. It doesn't matter; this is triangle ABC labeled the usual way.

c = 10, B = 35°, C = 65°

We have two angles and a side. The third angle is obviously

A = 180° - 35°- 65° = 80°

The remaining sides are given by the Law of Sines,

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

`a = (c \sin A)/(\sin C) = (10 \sin 80)/(\sin 65) = 10.866`

`b = (c \sin B)/(\sin C) = (10 \sin 35)/(\sin 65) = 6.328`

Answer: A=80°, a=10.9, b=6.3, third choice