Law Of Sines

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: $$\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}$$ .

BC = 24.

AC = 27.

Angle A = 78 degrees.

$$\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}$$ .

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

$$\sin(30^{\circ}) = \frac{1}{2}$$ .

The Law of Sines shows that the ratio of each side to the sine of its opposite angle is equal, allowing for the calculation of unknown sides or angles.

By rearranging the Law of Sines formula, you can solve for an unknown angle using the known sides and angles.

Using the Law of Sines, $$\sin(B) = \frac{b \cdot \sin(A)}{a}$$ .