Question

given right triangle qrs, what is the value of sin(30°)?
option 1: \\(\frac{\sqrt{3}}{3}\\)
option 2: \\(\frac{1}{2}\\)
option 3: \\(\frac{\sqrt{3}}{2}\\)
option 4: \\(\frac{2}{1}\\)

Explanation:

Step1: Recall sine definition

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle S=30^\circ$

Opposite side to $30^\circ$ is $QR=5$, hypotenuse is $QS=10$.

Step3: Calculate $\sin(30^\circ)$

$\sin(30^\circ) = \frac{5}{10} = \frac{1}{2}$

Answer:

$\boldsymbol{\frac{1}{2}}$ (corresponding to the option: $\boldsymbol{\frac{1}{2}}$)