Question

Given the diagram below, what is sin (30°) ?O A.OB.O C.OD. /3141411260°930°Triangle not drawn to scale

Answer 1

Given:

Using the trigonometric identity of sine;

`\begin{gathered} sin\theta=(opposite)/(hypotenuse) \\ where: \\ opposite=x \\ hypotenuse=9 \\ \theta=30^0 \\ \\ Hence, \\ sin30=(x)/(9) \\ From\text{ trigonometric tables;} \\ sin30=(1)/(2) \\ Hence, \\ (1)/(2)=(x)/(9) \\ Cross\text{ multiplying;} \\ 2x=9 \\ Dividing\text{ both sides by 2,} \\ x=(9)/(2) \end{gathered}`

Hence, the value of sin 30 is;

`\begin{gathered} sin(30^0)=(opposite)/(hypotenuse) \\ sin(30^0)=(x)/(9) \\ But\text{ }x=(9)/(2) \\ Thus; \\ sin(30^0)=((9)/(2))/(9) \\ sin(30^0)=(9)/(2)/9 \\ sin(30^0)=(9)/(2)*(1)/(9)=(9)/(18) \\ sin(30^0)=(1)/(2) \end{gathered}`

Therefore,

`sin(30^0)=(1)/(2)`

The correct answer is OPTION B.