Question

silas is at junction a along the road ab moving towards c. if he takes the shortest route from a to c, what distance will he cover? a $\frac{80}{sin 34}$ b $\frac{cos 34}{80}$ c $\frac{sin 34}{80}$ d $80 cos 34$ e $80 sin 34$

Explanation:

Step1: Identify the trigonometric relationship

In right - triangle \(ABC\), \(\angle C = 34^{\circ}\), \(AB = 80m\). We know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 34^{\circ}\), the opposite side to \(\angle C\) is \(AB\), and the hypotenuse is \(AC\).
So, \(\sin34^{\circ}=\frac{AB}{AC}\).

Step2: Solve for \(AC\)

From \(\sin34^{\circ}=\frac{80}{AC}\), we can cross - multiply to get \(AC\times\sin34^{\circ}=80\). Then, \(AC = \frac{80}{\sin34^{\circ}}\).

Answer:

A. \(\frac{80}{\sin34}\)