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:

$\cot A=\frac{24}{7}=\frac{adjacent}{opposite}$

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

$\begin{gathered} \sin A=\frac{opposite}{hypotenuse} \\ \\ \sin A=\frac{7}{25} \end{gathered}$