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**How to construct an angle without a protractor**

The Tangent Method How to construct an angle without a protractor

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**How it Works From the definition of tangent:**

The ratio of the sides of a right triangle are named sin, cos, and tan. SOHCOATOA From the definition of tangent: This simple fact is the basis of the Tangent Method. Any distance for x and it would work, but we chose 10 cm because it’s easy and fits on a piece of graph paper nicely.

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**How to use the Tangent Method**

Use your calculator to find the tangent of the angle you wish to construct. Multiply the tangent of the angle by 10 cm. Draw a 10 cm line horizontally on your graph paper. Now draw a vertical line from the right tip of the horizontal line the number of centimeters you calculated in Step 2. Connect the two end points to form a right triangle. The hypotenuse and the horizontal line form the desired angle.

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**Use the tangent method to draw an angle of 37 degrees.**

Example Use the tangent method to draw an angle of 37 degrees.

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**Step 1: Use a calculator to find the tangent of 37 degrees**

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**Step 2: Multiply the tangent of 37 degrees by 10**

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**Step 3: On graph paper, measure out 10 centimeters horizontally**

10 cm

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**Step 4: Measure out vertically the number of centimeters found in Step 2**

In step 2, we found that 7.54 cm 10 cm

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**Step 5: Connect the endpoints. You now have a line at the desired angle.**

7.54 cm This angle is 37 degrees 10 cm

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