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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

solve triangle ABC c 10 B 35 C 65 Question options A 80 a 10 b 63 A 80 a 63 b 109 A 80 a 109 b 63 A 80 a 736 b 63 class=

Respuesta :

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

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