Consider a triangle $\triangle ABC$. It is given that angle $A\hat{B}C$ is 38 degrees, angle $A\hat{C}B$ is 62 degrees, the length of $\overline{BC}$ is 38 cm. Find the perpendicular height of the triangle (from A to the base BC).

I can solve this with the use of Sine Rule. But is there another way to solve this question without using Sine Rule?