- Objectives
- Overview
- 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
- Worksheets
- Review Questions
- Chapter Exercises
This chapter is from the book
This chapter is from the book
This chapter is from the book
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.
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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 
, find the natural tangent of 
, which is 0.6128. Then, 
.
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 
sin θ. Draw the other side of the angle tangent to the arc, as shown.
Example To set off 
, find the natural sine of 
, which is 0.4305. Then 
.
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 
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 
. The sine of )
for a 1 unit radius. For a 10 unit radius, 
units.
Example To set off 
, the chordal length C for 1 unit radius, as given in a table of chords, equals 0.7384. If 
units, then 
units.