Let, d be the length of the side that divide the right triangle. Then, the area of the triangles are,
1/2 * b * d * sin(𝛳) and 1/2 * h * d * sin(90 - 𝛳), where d is unknown.
The total area is 1/2 * b * h.
So,
1/2 * b * d * sin(𝛳) + 1/2 * h * d * sin(90 - 𝛳) = 1/2 * b * h.
By solving this equation, we can find d, hence area of the both triangle.
N.B: The trigonometric functions take parameter in radian.