To help you effectively, I will first analyze the content of the uploaded image. I'll extract the mathematical problems and then solve them using the concepts of trigonometry, specifically the "TOA CAH SOH" mnemonic for sine, cosine, and tangent functions.

Let me process the image.The image contains two questions related to the diagrams of a cuboid and a prism.

Question 1 (a)

• Diagram: A cuboid is shown.
• Task: Calculate the length of $\overline{BD}$, which appears to be the diagonal of the rectangular face $ABCD$.

Question 1 (b)

• Task: Calculate the angle $\angle BDC$ between $\overline{BD}$ and $\overline{DC}$.

Question 2 (a)

• Diagram: A rectangular prism is shown.
• Task: Calculate the length of $\overline{DB}$, which seems to be the diagonal within the 3D shape from vertex $D$ to vertex $B$.

Question 2 (b)

• Task: Find the size of $\angle DBC$, where $B$ is a point where edges meet within the prism, likely involving 3D trigonometry.

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Solution Strategy:

1. For Question 1(a): Use the Pythagorean theorem to find $\overline{BD}$ on the rectangle $ABCD$.
2. For Question 1(b): Use trigonometric ratios (TOA CAH SOH) to find $\angle BDC$ after identifying the right triangle involved.
3. For Question 2(a): Apply the 3D Pythagorean theorem to determine $\overline{DB}$.
4. For Question 2(b): Use trigonometry to find the angle $\angle DBC$ considering the appropriate right triangle within the prism.

TOA CAH SOH Recap:

• TOA: Tangent = Opposite / Adjacent
• CAH: Cosine = Adjacent / Hypotenuse
• SOH: Sine = Opposite / Hypotenuse

Would you like me to go through each question step by step, starting with the calculation of $\overline{BD}$ in Question 1(a)?