Convert from rectangular coordinates <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mstyle></math> to polar coordinates <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> using the conversion formulas.

Replace <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> with the actual values.

Raise <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>135</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>18225</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>18250</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>730</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>18250</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Replace <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> with the actual values.

The inverse tangent of <math><mstyle displaystyle="true"><mn>27</mn></mstyle></math> is <math><mstyle displaystyle="true"><mi>θ</mi><mo>=</mo><mn>87.8789036</mn><mi>°</mi></mstyle></math> .

This is the result of the conversion to polar coordinates in <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> form.

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