Question

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

Answer 1

Solution:

Given:

Using the trigonometric identity of sine;

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

Hence, the value of sin 30 is;

$\begin{gathered} sin(30^0)=\frac{opposite}{hypotenuse} \\ sin(30^0)=\frac{x}{9} \\ But\text{ }x=\frac{9}{2} \\ Thus; \\ sin(30^0)=\frac{\frac{9}{2}}{9} \\ sin(30^0)=\frac{9}{2}\div9 \\ sin(30^0)=\frac{9}{2}\times\frac{1}{9}=\frac{9}{18} \\ sin(30^0)=\frac{1}{2} \end{gathered}$

Therefore,

$sin(30^0)=\frac{1}{2}$

The correct answer is OPTION B.