Question

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

Answer 1

Option b

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:

`(sin(A))/(a) = (sin(B))/(b) = (sin(C))/(c)`

Then:

`(sin(92))/(4.6) = (sin(19))/(b)\\\\b = (sin(19))/((sin(92))/(4.6))\\\\b = 1.5`

`(sin(B))/(b) = (sin(C))/(c)\\\\(sin(19))/(1.5) = (sin(69))/(c)\\\\c = (sin(69))/((sin(19))/(1.5))\\\\c = 4.30`