Question

sina = \frac{b}{c}
sina = \frac{h}{c}
sinc = \frac{b}{a}
sinc = \frac{a}{h}

Explanation:

Step1: Recall the definition of sine in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Identify the sides relative to angle \(A\)

For the right - triangle formed with angle \(A\), the opposite side to angle \(A\) is \(h\) and the hypotenuse is \(c\). So, \(\sin A=\frac{h}{c}\).

• For option A: \(\sin A=\frac{b}{c}\) is incorrect. In a right - triangle, \(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{b}{c}\) (where \(b\) is the adjacent side to angle \(A\) and \(c\) is the hypotenuse).
• For option C: \(\sin C=\frac{b}{a}\) is incorrect. For the right - triangle formed with angle \(C\), \(\sin C=\frac{h}{a}\) (opposite side \(h\) and hypotenuse \(a\)).
• For option D: \(\sin C=\frac{a}{h}\) is incorrect. Since \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), and for angle \(C\) the opposite side is \(h\) and hypotenuse is \(a\), so it should be \(\sin C = \frac{h}{a}\) not \(\frac{a}{h}\).

Answer:

B. \(\sin A=\frac{h}{c}\)