Question

find sin a, and write your answer as a fraction in lowest terms.

a
33
55
c
44
b

a. sin a = \frac{4}{3}
b. sin a = \frac{5}{4}
c. sin a = \frac{3}{5}
d. sin a = \frac{4}{5}

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(A\), the side opposite to angle \(A\) is \(BC = 44\), and the hypotenuse \(AB=55\).

Step2: Calculate \(\sin A\)

\(\sin A=\frac{BC}{AB}=\frac{44}{55}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of \(44\) and \(55\) is \(11\). So, \(\frac{44\div11}{55\div11}=\frac{4}{5}\).

Answer:

D. \(\sin A=\frac{4}{5}\)