Question

directions: solve for the missing side. round to the tenths place. * find a missing

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 40^{\circ}\), the hypotenuse \(c = 10\), and the opposite side to the \(40^{\circ}\) angle is \(x\). So, \(\sin40^{\circ}=\frac{x}{10}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin40^{\circ}=\frac{x}{10}\) by \(10\). We get \(x = 10\times\sin40^{\circ}\). Since \(\sin40^{\circ}\approx0.6428\), then \(x=10\times0.6428 = 6.428\). Rounding to the tenths place, \(x\approx6.4\).

Answer:

\(6.4\)