Question: c) \[ \begin{array}{c} \text{6.4 m} \\ \text{18°} \\ \text{v} \end{array} \] \[…

c)

\[ \begin{array}{c} \text{6.4 m} \\ \text{18°} \\ \text{v} \end{array} \]

\[ \text{hyp} \]

\[ \text{opp} \]

\[ \text{tan} = \frac{\text{opp}}{\text{adj}} \]

Solution

To solve for \( v \) in the right triangle, we can use the sine function since we have the angle and the hypotenuse. The sine function is defined as: \[ \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}} \] Here, the angle is \(18^\circ\), the hypotenuse is \(6.4 \, \text{m}\), and the opposite side is \(v\). Start by writing the equation for \(\sin(18^\circ)\): \[ \sin(18^\circ) = \frac{v}{6.4} \] Rearrange the equation to solve for \(v\): \[ v = 6.4 \cdot \sin(18^\circ) \] Calculate \(\sin(18^\circ)\) using a calculator: \[ v = 6.4 \cdot 0.3090 \] Multiply to find \(v\): \[ v \approx 1.9776 \] Thus, the length of \(v\) is approximately \(1.98 \, \text{m}\).