SOLUTION: I would really appreciate some help with this question, please help me. Thank you . Construct accurately ∆ABC𝐴𝐵𝐶 where AB 𝐴𝐵 = 6cm&#

Algebra ->  Trigonometry-basics -> SOLUTION: I would really appreciate some help with this question, please help me. Thank you . Construct accurately ∆ABC𝐴𝐵𝐶 where AB 𝐴𝐵 = 6cm&#      Log On


   

Question 1089596: I would really appreciate some help with this question, please help me.
Thank you .
Construct accurately ∆ABC𝐴𝐵𝐶 where AB 𝐴𝐵 = 6cm∠CAB𝐶𝐴𝐵 = 70°, and ∠ = 𝐴𝐵𝐶 = 65°
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Drawing this helps.
Angle C must be 45 degrees.
use law of sines
a/sin A=b/sin B=c/sin C
c=6
6/sin 45=6/sqrt(2)=8.49
Therefore
8.49=a/sin A and a=8.49 sin 70=7.98 cm for a
b/sin B=8.49=b/sin 65
b=8.49*sin 65=7.69 cm.
Can be fancy and check one using law of cosines.
a^2=b^2+c^2-2bc cos A=59.2+36-2(6*7.69)cos 70
that is 95.2-92.28*cos 70=95.2-31.56=63.64, which is a^2
a=7.98
so a=7.98, b=7.69 c=6