Question

write the ratios for sin a and cos a.
not drawn to scale
sin a = \frac{35}{37}, cos a = \frac{12}{35}
sin a = \frac{35}{37}, cos a = \frac{12}{37}
sin a = \frac{35}{12}, cos a = \frac{12}{37}
sin a = \frac{12}{37}, cos a = \frac{35}{37}

Explanation:

Step1: Recall the definitions of sine and cosine in a right - triangle

In a right - triangle, for an angle \(A\), \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}\).
For angle \(A\) in \(\triangle ABC\) with right - angle at \(C\), the side opposite to angle \(A\) is \(BC = 35\), the side adjacent to angle \(A\) is \(AC=12\), and the hypotenuse \(AB = 37\).

Step2: Calculate \(\sin A\) and \(\cos A\)

Using the definitions:
\(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{BC}{AB}=\frac{35}{37}\)
\(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{AC}{AB}=\frac{12}{37}\)

Answer:

\(\sin A=\frac{35}{37},\cos A=\frac{12}{37}\) (the second option)