`A = 36^@, a = 8, b = 5` Use the law of sines to solve the triangle. (Find missing sides/angles) Round answers to 2 decimal places.

The sine law indicates that in a triangle;

`(sinA)/a =(sinB)/b =(sinC)/c`

a,b,c are the lengths of the triangle and A,B,C are the opposite angles as shown in image.

`(sinA)/a =(sinB)/b`

`sin36/8 = sinB/5`

`B = sin^(-1)(sin36xx5/8) = 21.55^0`

Angle C `= 180-21.55-36 = 122.45^0`

`(sinB)/b =(sinC)/c`

`c = (sin122.45xx5)/sin21.55 = 11.49`

So the answers are;

Angle B = 21.55 deg

Angle C = 122.45 deg

Length c = 11.49 units

...

The sine law indicates that in a triangle;

`(sinA)/a =(sinB)/b =(sinC)/c`

a,b,c are the lengths of the triangle and A,B,C are the opposite angles as shown in image.

`(sinA)/a =(sinB)/b`

`sin36/8 = sinB/5`

`B = sin^(-1)(sin36xx5/8) = 21.55^0`

Angle C `= 180-21.55-36 = 122.45^0`

`(sinB)/b =(sinC)/c`

`c = (sin122.45xx5)/sin21.55 = 11.49`

So the answers are;

Angle B = 21.55 deg

Angle C = 122.45 deg

Length c = 11.49 units