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,
Mathematics
gavinsskyler
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
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
1 Answer

1. User Answers DeanR
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,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]a = \dfrac{c \sin A}{\sin C} = \dfrac{10 \sin 80}{\sin 65} = 10.866[/tex]
[tex]b = \dfrac{c \sin B}{\sin C} = \dfrac{10 \sin 35}{\sin 65} = 6.328[/tex]
Answer: A=80°, a=10.9, b=6.3, third choice