Question

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.

Answer 1

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}`