Question

question 2 (5 points)
listen
a right triangle has the hypotenuse ( c = 12 mathrm{cm} ) and an angle ( a = 30^{circ} ). find the length
of side ( a ), which is opposite angle ( a ).
a) ( 7.4 mathrm{cm} )
b) ( 2.5 mathrm{cm} )
c) ( 6 mathrm{cm} )
d) ( 4 mathrm{cm} )

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin A=\frac{a}{c}\), where \(a\) is the side opposite angle \(A\) and \(c\) is the hypotenuse.

Step2: Substitute the given values

Given \(c = 12\space\text{cm}\) and \(A = 30^{\circ}\), and \(\sin30^{\circ}=\frac{1}{2}\). Substituting into \(\sin A=\frac{a}{c}\), we get \(\frac{1}{2}=\frac{a}{12}\).

Step3: Solve for \(a\)

Cross - multiply: \(a = 12\times\frac{1}{2}\).

Answer:

\(a = 6\space\text{cm}\), so the answer is C.