Question

use a calculator to find the length of each side. round to 4 decimal places.
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Explanation:

Step1: Find the length of side \(a\)

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 12^{\circ}\) and the hypotenuse \(c = 10\). For side \(a\) (opposite to the \(12^{\circ}\) angle), we have \(a = c\times\sin\theta\).
Substitute \(c = 10\) and \(\theta=12^{\circ}\) into the formula: \(a = 10\times\sin(12^{\circ})\).
Using a calculator, \(\sin(12^{\circ})\approx0.2079\), so \(a=10\times0.2079 = 2.0791\).

Step2: Find the length of side \(b\)

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 12^{\circ}\) and the hypotenuse \(c = 10\). For side \(b\) (adjacent to the \(12^{\circ}\) angle), we have \(b = c\times\cos\theta\).
Substitute \(c = 10\) and \(\theta = 12^{\circ}\) into the formula: \(b=10\times\cos(12^{\circ})\).
Using a calculator, \(\cos(12^{\circ})\approx0.9781\), so \(b = 10\times0.9781=9.7812\).

Answer:

\(a = 2.0791\), \(b = 9.7812\)