Sine-Law
\(\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}\)
Let the Capital "A" be the angle we want.
Let "a" be the side opposite to angle A (I.e. BC)
Let Capital "B" be 123 degrees angle (As given)
Let "b" be the side opposite to angle B (I.e. AC)
Let capital "C" be the angle on the left.
Let "c" be the side opposite to angle "C" (I.e. AB)
Substitute the given information into the law
Given:
Angle B=123 degrees
a=19
b=43
\(\frac{sin(A)}{19}=\frac{sin(123)}{43}\) ...
We don't know anything about C nor c thus we don't need it.
We are trying to find angle A
Notice that (Cross-multiplication)
\(43*sin(A)=19*sin(123)\)
\(sin(A)=\frac{19*sin(123)}{43}\)
A=\(sin^{-1}(\frac{19*sin(123)}{43})\)
Use a calculator to evaluate.
A=21.75 correct to 2 decimal place.
A=21.8 correct to 1 decimal place.
A=22 correct to the nearest integer
