Question

→ make sure your calculator is in degree mode
example 1: find the length of side ac using trig ratios. round final answer to 1 decimal place.

Explanation:

Step1: Identify the trig - ratio

In right - triangle \(ABC\) with right - angle at \(C\), we know the hypotenuse \(AB = 12\) cm and we want to find the side \(AC\) opposite to the angle \(B=25^{\circ}\). The sine ratio is used as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
\(\sin B=\frac{AC}{AB}\)

Step2: Substitute the values

We know \(B = 25^{\circ}\) and \(AB = 12\) cm. So, \(AC=AB\times\sin B\).
\(AC = 12\times\sin(25^{\circ})\)

Step3: Calculate the value

Using a calculator in degree mode, \(\sin(25^{\circ})\approx0.4226\). Then \(AC = 12\times0.4226 = 5.0712\) cm.

Step4: Round the answer

Rounding to 1 decimal place, \(AC\approx5.1\) cm.

Answer:

\(5.1\) cm