Question

13 multiple choice 1 point
write the ratios for sin a and cos a.

hint: sohcahtoa

sin a = \frac{63}{10}, cos a = \frac{16}{63}

sin a = \frac{63}{65}, cos a = \frac{16}{65}

sin a = \frac{16}{65}, cos a = \frac{63}{65}

sin a = \frac{63}{65}, cos a = \frac{16}{65}

Explanation:

Step1: Recall the definitions of sine and cosine

In a right - triangle, \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}\).
For angle \(A\), the side opposite to \(A\) is \(BC = 63\), the side adjacent to \(A\) is \(AC=16\), and the hypotenuse \(AB = 65\) (using the Pythagorean theorem \(16^{2}+63^{2}=256 + 3969=4225=65^{2}\)).

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

\(\sin A=\frac{BC}{AB}=\frac{63}{65}\)
\(\cos A=\frac{AC}{AB}=\frac{16}{65}\)

Answer:

\(\sin A=\frac{63}{65},\cos A=\frac{16}{65}\) (the second option)