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Given Cot A = 24/7 and that angle A is in Quadrant I find the exact value of sin A in simplest radical form using a rational denominator.

User Eric Urban
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1 Answer

1 vote

Given:


\cot A=(24)/(7)=(adjacent)/(opposite)

so, the opposite to the angle A = 7

The adjacent to the angle A = 24

Using the Pythagorean theorem to find the hypotenuse


\text{hypotenuse}=\sqrt[]{7^2+24^2}=\sqrt[]{49+576}=\sqrt[]{625}=25

The angle A is in Quadrant I, so the sin will be positive


\begin{gathered} \sin A=(opposite)/(hypotenuse) \\ \\ \sin A=(7)/(25) \end{gathered}

User Zmeda
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