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));
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).`