To find the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> between the x-axis and the line between the points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><msqrt><mn>11</mn></msqrt></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> , draw the triangle between the three points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><msqrt><mn>11</mn></msqrt></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Opposite : <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>11</mn></msqrt></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>

Adjacent : <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><msqrt><mn>11</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

Approximate the result.

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