1. **Stating the problem:** We have a triangular pyramid with vertices A, B, C, and D. Given angles are $\angle D = 39^\circ$, $\angle A = 44^\circ$, and $\angle BAC = 126^\circ$. The length $BC = 46$ cm. At vertex B, there is a right angle between the vertical line from D to B and the horizontal line from B to C. We want to find unknown lengths or angles related to this pyramid. 2. **Understanding the geometry:** The right angle at B between $DB$ and $BC$ means $DB \perp BC$. The angle $BAC = 126^\circ$ is the angle at A between points B and C. 3. **Using the Law of Cosines in triangle ABC:** To find side $AB$ or $AC$, we use the formula: $$c^2 = a^2 + b^2 - 2ab \cos(C)$$ where $C$ is the angle opposite side $c$. 4. **Assigning sides:** Let $AB = x$, $AC = y$, and $BC = 46$ cm. The angle at A is $44^\circ$, and the angle between BA and BC at B is $90^\circ$, so we can use trigonometry to find lengths. 5. **Using right triangle at B:** Since $DB \perp BC$, and $\angle D = 39^\circ$, we can find the height $DB$ using trigonometric relations if more data is given. 6. **Summary:** Without additional lengths or specific questions, the problem is to analyze the pyramid using given angles and side $BC = 46$ cm. Since the user did not specify what to find, we can calculate the length $AB$ using the Law of Cosines in triangle ABC with $\angle BAC = 126^\circ$: $$AB^2 = BC^2 + AC^2 - 2 \times BC \times AC \times \cos(126^\circ)$$ But $AC$ is unknown, so we need more data to proceed. **Final note:** Please provide which length or angle to find or more data to solve completely.