Question

Solve the triangle that has a=4.6, B=19°, A=92° (picture provided)

Answer 1

Answer:

Option b

Step-by-step explanation:

To solve this problem use the law of the sines.

We have 2 angles of the triangle and one of the sides.

$a = 4.6\\B = 19\°\\A = 92\°\\C = 180 -A - B\\C = 180 - 92 - 19\\C = 69\°$

The law of the sines is:

$\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}$

Then:

$\frac{sin(92)}{4.6} = \frac{sin(19)}{b}\\\\b = \frac{sin(19)}{\frac{sin(92)}{4.6}}\\\\b = 1.5$

$\frac{sin(B)}{b} = \frac{sin(C)}{c}\\\\\frac{sin(19)}{1.5} = \frac{sin(69)}{c}\\\\c = \frac{sin(69)}{\frac{sin(19)}{1.5}}\\\\c = 4.30$