# `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.

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Expert Answers

jeew-m | Certified Educator

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**

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