Question

b) 16 cm 57° x

Explanation:

Step1: Identify the trigonometric ratio

In a right - angled triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 57^{\circ}\), the side opposite to \(57^{\circ}\) is \(16\) cm and the hypotenuse is \(x\).
So, \(\sin57^{\circ}=\frac{16}{x}\)

Step2: Solve for \(x\)

We know that \(\sin57^{\circ}\approx0.8387\) (a known value from trigonometric tables or calculator).
From \(\sin57^{\circ}=\frac{16}{x}\), we can rewrite it as \(x=\frac{16}{\sin57^{\circ}}\)
Substitute \(\sin57^{\circ}\approx0.8387\) into the equation: \(x=\frac{16}{0.8387}\approx19.1\)

Answer:

\(x\approx19.1\) cm