Question

12 multiple choice 1 point
write the ratios for sin a and cos a.
not drawn to scale
sin a = \frac{63}{16}, cos a = \frac{16}{65}
sin a = \frac{63}{65}, cos a = \frac{16}{63}
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

In a right - triangle, for an acute angle \(A\), \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Identify the sides relative to angle \(A\)

The side opposite to angle \(A\) is \(BC = 63\), the side adjacent to angle \(A\) is \(AC=16\), and the hypotenuse \(AB = 65\).

Step3: Calculate \(\sin A\) and \(\cos A\)

Using the definitions:

• \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{BC}{AB}=\frac{63}{65}\)
• \(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{AC}{AB}=\frac{16}{65}\)

Answer:

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