SOLUTION: determine the number of triangles with the given part: if possible, solve each triangle: B: 146.4 ° c: 7.7 b: 14.4

Algebra ->  Trigonometry-basics -> SOLUTION: determine the number of triangles with the given part: if possible, solve each triangle: B: 146.4 ° c: 7.7 b: 14.4      Log On


   

Question 1131836: determine the number of triangles with the given part: if possible, solve each triangle:
B: 146.4 °
c: 7.7
b: 14.4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

solve triangle with:
b=14.4+
c=7.7
B=146.4°


use the Law of Sines to find angle C
c%2Fsin%28C%29=b%2Fsin%28B%29
7.7%2Fsin%28C%29=14.4%2Fsin%28146.4%29
C=sin%5E-1%28+%287.7+%2A+sin%28+146.4+%29%29+%2F+14.4+%29+
C=sin%5E-1%28+%287.7+%2A+0.553392%29+%2F+14.4+%29+
C=sin%5E-1%284.2611184%2F14.4%29
C=sin%5E-1%280.295911%29
C=17.21°
and use the sum of the angles in triangle to find angle A
A=180-%28146.4%2B17.21%29°
A=180-163.61°
A=16.39°
use the Law of sines to find side a
a%2Fsin%2816.39%29=14.4%2Fsin%28146.4%29
a%2F0.282174=14.4%2F0.553392
a%2F0.282174=26.0213374967473328
a=26.0213374967473328%2A0.282174
a=7.3425
a=7.34