1. State the problem: Given an isometric sketch of a solid, produce its oblique sketch using an oblique projection method. 2. Formula and projection rule: $$ (x',y') = (x + l\cos\theta\, z,\; y + l\sin\theta\, z) $$ This maps a 3D point $x,y,z$ to a 2D point $x',y'$ in an oblique projection. 3. Important rules: - Draw the front face in true size because oblique keeps the front face undistorted. - Choose a receding direction given by angle $\theta$ measured from the horizontal and a receding scale $l$; common choices are $\theta=45^\circ$ and $l=\frac{1}{2}$ (cabinet). 4. Construction steps to convert the given isometric sketch to an oblique sketch: - Identify the front face in the isometric view and sketch it as a rectangle (or square) in true size on your paper. - Choose $\theta$ and $l$; for clarity use $\theta=45^\circ$ and $l=\frac{1}{2}$ unless the problem specifies otherwise. - For each vertex of the front face, draw a receding line at angle $\theta$ from the horizontal and measure along it the depth component scaled by $l$ for the corresponding 3D depth. - Mark the endpoints of those receding segments and connect them to complete the top and side faces; edges parallel to front-face edges remain parallel in the oblique sketch. - Darken visible edges and use dashed lines for hidden edges if required. 5. Example (illustration of the numeric mapping): Assume a point at $(x,y,z)=(2,1,3)$, $\theta=45^\circ$, $l=\frac{1}{2}$. Compute $\cos45^\circ=\frac{\sqrt{2}}{2}$ and $\sin45^\circ=\frac{\sqrt{2}}{2}$. Then $x'=2 + \frac{1}{2}\cdot\frac{\sqrt{2}}{2}\cdot 3 = 2 + \frac{3\sqrt{2}}{4}$ and $y'=1 + \frac{1}{2}\cdot\frac{\sqrt{2}}{2}\cdot 3 = 1 + \frac{3\sqrt{2}}{4}$. 6. Tips for neatness: Use a ruler for true-size front face, use consistent scale for depth, and label dimensions. Final answer: The oblique sketch is produced by drawing the front face in true size and projecting receding edges at angle $\theta$ with scale $l$ using the formula above; using $\theta=45^\circ$ and $l=\frac{1}{2}$ gives a standard cabinet oblique.