How to Measure an Angle Between Two Points
Measuring an angle between two points is an important component of geometry. In order to measure an angle between two points, you must choose a third point from which to measure the angle. For instance, if measuring the angle between two points on a circle, choose the center of the circle as the third point from which to measure the angle. After choosing this third point, you can use either a protractor or trigonometry to measure the angle between the two points.
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Instructions
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Protractor
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1
Draw a line between the first point and the point from which the angle will be measured. Use a ruler for this step to ensure the line is straight. Next, draw a line between the second point and the point from which the angle will be measured.
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2
Find the center hole on the straight edge of the protractor. Place the center hole over the point from which you plan to measure the angle.
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3
Line up the straight edge of the protractor with one of the lines that you drew in Step 1.
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4
Use a ruler to extend the other line, until the line intersects with the curved edge of the protractor.
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5
Read the angle that is written on the protractor that corresponds to the point of intersection between the protractor and the line you extended in Step 4. This number is the measure of the angle.
Measuring an Angle Using Trigonometry
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6
Draw lines connecting the two points and the third point from which you plan to measure the angle. Use a ruler for this step to ensure the line is as straight as possible. When finished, observe that a triangle is formed.
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7
Use a ruler to measure the lengths of all three lines.
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8
Calculate the value of the sine, cosine, or tangent of the angle, depending on your preferences. The sine of an angle is equal to the length of the side opposite of the angle, divided by the length of the triangle's hypotenuse, or longest side. The cosine of the angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse of the triangle. The tangent of an angle is equal to the length of the side opposite of the angle divided by the length of the side adjacent to the angle.
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9
Use a graphing calculator to obtain the inverse sine, inverse cosine, or inverse tangent of the calculation that you made in Step 3. This value is equal to the magnitude of your angle.
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References
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