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, we use the sine function. The formula for sine is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 12^{\circ}\) and the hypotenuse \(c = 10\). So, \(a = 10\times\sin(12^{\circ})\). Using a calculator, \(\sin(12^{\circ})\approx0.2079\), then \(a = 10\times0.2079 = 2.0791\).

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

In a right - triangle, we use the cosine function. The formula for cosine is \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 12^{\circ}\) and the hypotenuse \(c = 10\). So, \(b = 10\times\cos(12^{\circ})\). Using a calculator, \(\cos(12^{\circ})\approx0.9781\), then \(b = 10\times0.9781=9.7812\).

Answer:

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