Question

determine \\(\sin(a)\\) and \\(\sin(b)\\).
a) \\(\sin(a)\\)
b) \\(\sin(b)\\)

Explanation:

Step1: Recall Sine Definition

In a right triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\triangle ABC\) (right - angled at \(C\)):

• For \(\sin(A)\): The angle is \(A\), the side opposite to \(A\) is \(BC = 16\), and the hypotenuse is \(AB=34\).

Step2: Calculate \(\sin(A)\)

Using the sine formula, \(\sin(A)=\frac{BC}{AB}=\frac{16}{34}=\frac{8}{17}\).

Step3: Calculate \(\sin(B)\)

For angle \(B\), the side opposite to \(B\) is \(AC = 30\), and the hypotenuse is \(AB = 34\). So, \(\sin(B)=\frac{AC}{AB}=\frac{30}{34}=\frac{15}{17}\).

Answer:

a) \(\sin(A)=\frac{8}{17}\)
b) \(\sin(B)=\frac{15}{17}\)