#1**0 **

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

Guest Jan 30, 2020