A scalene triangle given sides A, side B, and angle a (in radian). Asking for angle b in radian? why The answer is = pi - asin(B/A sin a);Why the answer is pi - asin(B/A sin a); I thought angle b...

A scalene triangle given sides A, side B, and angle a (in radian). Asking for angle b in radian? why The answer is = pi - asin(B/A sin a);

Why the answer is pi - asin(B/A sin a); I thought angle b is just asin(B/A sin a) (using law of sin).

sin(a)/A = sin(b)/B => b= asin(B/A sin(b));

sciencesolve | Certified Educator

You should use the law of sines but you also need to remember that the sum of angles of triangle is `180^o = pi`  radians.

Using the law of sines yields:

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

The problem provides the values of lengths of sides A and B and the measure of angle a such that:

`sin a/A = sin b/B => A sin b = B sin a => sin b = (B sin a)/A => b = arcsin ((B sin a)/A)`

You should use the property that the sum of interior angles of triangle yields `pi`  such that:

`a+b+c = pi => b = pi - (a+c)`

Equating `b = pi - (a+c)`  and `b = arcsin ((B sin a)/A)`  yields:

`pi - (a+c) = arcsin ((B sin a)/A) => a+c = pi - arcsin ((B sin a)/A)`

Since it's missing an information, such as `a+c = pi - arcsin ((B sin a)/A)`  or the value of angle c or the lenght of side C, you may state that the answer `pi - arcsin ((B sin a)/A)`  is only equal to the sum of the other two interior angles of triangle such that `a+c = pi - arcsin ((B sin a)/A).`