Question

d. 35 yards 18° 44.5 yards 44° x plan of attack: solve for x:

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(A\). Then \(A = 180^{\circ}-(18^{\circ}+44^{\circ})=118^{\circ}\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Here, we want to find \(x\). Using \(\frac{35}{\sin44^{\circ}}=\frac{x}{\sin18^{\circ}}\) (cross - multiply).

$$x=\frac{35\times\sin18^{\circ}}{\sin44^{\circ}}$$

Step3: Calculate the sine values

We know that \(\sin18^{\circ}\approx0.3090\) and \(\sin44^{\circ}\approx0.6947\).

$$x=\frac{35\times0.3090}{0.6947}$$

$$x=\frac{10.815}{0.6947}\approx15.6$$

Answer:

\(x\approx15.6\) yards