- Coordinates for 3D CAD Modeling
- Geometric Entities
- 4.1 Manually Bisecting a Line or Circular Arc
- 4.2 Drawing Tangents to Two Circles
- 4.3 Drawing an Arc Tangent to a Line or Arc and Through a Point
- 4.4 Bisecting an Angle
- 4.5 Drawing a Line through a Point and Parallel to a Line
- 4.6 Drawing a Triangle with Sides Given
- 4.7 Drawing a Right Triangle with Hypotenuse and One Side Given
- 4.8 Laying Out an Angle
- 4.9 Drawing an Equilateral Triangle
- 4.10 Polygons
- 4.11 Drawing a Regular Pentagon
- 4.12 Drawing a Hexagon
- 4.13 Ellipses
- 4.14 Spline Curves
- 4.15 Geometric Relationships
- 4.16 Solid Primitives
- 4.17 Recognizing Symmetry
- 4.18 Extruded Forms
- 4.19 Revolved Forms
- 4.20 Irregular Surfaces
- 4.21 User Coordinate Systems
- 4.22 Transformations
- Key Words
- Chapter Summary
- Skills Summary
- Review Questions
- Chapter Exercises

## 4.8 Laying Out an Angle

Many angles can be laid out directly with the triangle or protractor. For more accuracy, use one of the methods shown in Figure 4.31.

**4.31** Laying Out Angles

**Tangent Method** The tangent of angle θ is *y*/*x*, and *y* = *x* tan θ. Use a convenient value for *x*, preferably 10 units (Figure 4.31a). (The larger the unit, the more accurate will be the construction.) Look up the tangent of angle θ and multiply by 10, and measure *y* = 10 tan θ.

EXAMPLE To set off 31-1/2°, find the natural tangent of 31-1/2°, which is 0.6128. Then,

*y*= 10 units × 0.6128 = 6.128 units.**Sine Method**Draw line*x*to any convenient length, preferably 10 units (Figure 4.31b). Find the sine of angle θ, multiply by 10, and draw arc with radius*R*= 10 sin θ. Draw the other side of the angle tangent to the arc, as shown.EXAMPLE To set off 25-1/2°, find the natural sine of 25-1/2°, which is 0.4305. Then

*R*= 10 units × 0.4305 = 4.305 units.

**Chord Method** Draw line *x* of any convenient length, and draw an arc with any convenient radius *R*—say 10 units (Figure 4.31c). Find the chordal length *C* using the formula *C* = 2 sin θ/2. Machinists’ handbooks have chord tables. These tables are made using a radius of 1 unit, so it is easy to scale by multiplying the table values by the actual radius used.

EXAMPLE Half of 43°20′ = 21°40′. The sine of 21°40′ = 0.3692. C = 2 × 0.3692 = 0.7384 for a 1 unit radius. For a 10 unit radius, C = 7.384 units.

EXAMPLE To set off 43°20′, the chordal length

*C*for 1 unit radius, as given in a table of chords, equals 0.7384. If*R*= 10 units, then*C*= 7.384 units.