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How to Find the Height & Width if You Know the Diagonal

Basic math formulas have everyday applications outside the classroom that many people are unaware of. The same formulas that are used to calculate the height and width of a triangle given the diagonal can be applied to determining the size of computer monitors and television screens. By drawing out a diagram and by using the principles of algebra, it is possible to find out the height and width of a triangle, square, or rectangle given the diagonal.

Things You'll Need

  • Protractor
  • Graph paper
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Instructions

    • 1

      Determine the angle of the diagonal, if it isn't given, using a protractor. Set the bottom of the protractor on a flat surface and line up the center of the protractor with the bottom point of the diagonal. Trace the diagonal with your finger or use a ruler to find the corresponding angle on the protractor.

    • 2

      Decide on a scale to use for your diagram by assigning a value to each square. For example, you might decide that one square equals 1 inch. You will use this scale to determine the actual height and width of the shape once you have completed your diagram.

    • 3

      Draw out a diagram on a sheet of graph paper. Begin by drawing a horizontal line on the graph paper then draw out the diagonal using the horizontal line as the bottom point for the diagonal. Use your protractor to get the angle of the diagonal right and, using the scale you decided on, draw the diagonal to the appropriate length.

    • 4

      Draw a vertical line connecting the top point of the diagonal with the horizontal line. If the shape you are measuring is a triangle, your drawing should now look like that shape. If the shape you are measuring is a square or rectangle you will need to draw a vertical line up from the bottom point of the diagonal and connect it with a horizontal line to the top point of the diagonal.

    • 5

      Count the squares on the graph paper to determine the height and width of the shape. Multiply the number of squares for each measurement by the scale determined in Step 2. For example, if you decided that one square equals 1 inch and you counted 12 inches for the width, then your shape has a width of 12 inches.

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