How to Know That a Right Angle is a Right Angle

Written by steven j. wamback
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How to Know That a Right Angle is a Right Angle
Right angles help keep our homes plumb, level and square so doors and windows open and close smoothly and carpets fit neatly. (Thinkstock/Comstock/Getty Images)

Keep it plumb, level and square are the main rules of engineering, architecture, carpentry, wood working and home repairs. Each of these parameters is a function of right angles. Plumb means that that the work forms a right angle between horizontal and the centre of the Earth. Level means the work forms right angles with any perpendicular (plumb) lines. Square means the work forms right angles at all four corners. There are a few simple tools and easy calculations you can employ to ensure that any right angle in your life is truly a right angle or a right triangle.

Skill level:

Things you need

  • Carpenter's square
  • T-square
  • Drafting triangle (30-60-90)
  • Drafting triangle (45-45-90)
  • Protractor
  • Bubble level
  • Plumb bob

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  1. 1

    Use a carpenter's square to check the inside and outside right angles of cut lumber, lumber to be cut and finished corners of rooms or work pieces. Assume that the carpenter's square is a perfect right angle and is made to be used as your standard in designing and building projects. Simply hold the square up to the angle you wish to check. If it fits snugly with no excess space at the apex or out on the limbs, your right angle is truly a right angle.

    How to Know That a Right Angle is a Right Angle
    A carpenter's square or drafting square is really a precision scientific instrument used to check and draw right angles. (Jupiterimages/liquidlibrary/Getty Images)
  2. 2

    Create a set of plans for your next woodworking or home repair project using drafting tools such as protractors, triangles and T-squares. If you use an accurate scale and true right angles, your plans will be a very good representation of the actual finished project. Use the T-square to draw lines at right angles to other lines and use the drafting triangle to check your work and to draw right angles as well.

    How to Know That a Right Angle is a Right Angle
    Use drafting triangles, protractors, and squares to lay out project plans with perfect right angles. (Brand X Pictures/Brand X Pictures/Getty Images)
  3. 3

    Prove to yourself that right angles are 90 degrees; that all three angles of any triangle add up to 180 degrees; and that the two angles opposite a right angle always add up to 90 degrees. Use a protractor to measure all three angles on each of your two drafting triangles. One triangle will have two 45-degree angles and the 90-degree right angle. The other triangle will have a 30-degree angle, a 60-degree angle and the requisite 90 degree right angle. Use this principle to confirm right angles that you cannot measure directly. The opposite two angles should always add up to 90 degrees. If they do not, then your angle is not a right angle.

    How to Know That a Right Angle is a Right Angle
    All three angles of any triangle add up to 180 degrees. Right triangles have one 90-degree angle and two other angles that always add to to 90 degrees. (Hemera Technologies/ Images)
  4. 4

    Keep a variety of protractors available in your drafting and home repair tool kit. Use these for laying out plans with accurate angles and right angles both on paper and on lumber. Use your protractors also for measuring or checking any angles or right angles about which you are not sure. Remember the two angles opposite a right angle always add up to 90 degrees and the right angle itself is always 90 degrees.

    How to Know That a Right Angle is a Right Angle
    Use a protractor to measure unknown angles and to check right angles for accuracy. (Stockbyte/Stockbyte/Getty Images)
  5. 5

    Use a plumb bob (weight on a string) to check for the plumb of walls, fence posts and doorjambs. Plumb is the right angle formed between a horizontal (level) line and the centre of the Earth to which a plumb bob is always attracted by gravity. Create a level line by centring the bubble in a bubble level. Check for plumb by dropping a plumb bob from that line on a string. If the line is parallel to the work (wall, doorjamb or post) then you have an accurate right angle between the work and horizontal. Use a protractor to measure any error between a plumb line and your work.

    How to Know That a Right Angle is a Right Angle
    A plumb bob always forms an accurate right angle with a level horizontal surface from which it is dropped. (Jupiterimages/liquidlibrary/Getty Images)
  6. 6

    Use the Pythagorean Theorom to double check the accuracy of your right angles. The right angle is the basis of trigonometry and trigonometry is the mathematical way of ensuring that right angles are truly right angles. If A-squared plus B-squared equals C-squared turns out to be true for the sides of any triangle containing your right angle then you know your right angle is a right angle. Side C is always the side opposite the right angle. Use this formula to measure things indirectly such as the height of a tree, building or flagpole after measuring the length of its shadow and checking the right angle the object forms with the Earth.

    How to Know That a Right Angle is a Right Angle
    When all else fails, do the math. A-squared plus B-squared equals C-Squared will work if the right angle really is a right angle. (BananaStock/BananaStock/Getty Images)

Tips and warnings

  • Keep a special tool box for your drafting, measuring and work layout tools. Include such items as rulers, tape measures, levels, squares, triangles, protractors, plumb bobs, lasers, compasses, calipers, pencils, notebook, calculator and an engineering conversion table reference handbook. Use this special tool kit for planning, drafting, estimating, laying out projects, surveying, map-making, and helping kids with scouting, homework and school projects.
  • Keep your drafting, measuring, and layout tools clean and neat and well protected from damage. They are precision scientific instruments and will remain accurate as long as they are well taken care of.

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