Question

3. Solve using the Laws of Sines Make a drawing to graphically represent what the following word problem states. to. Two fire watch towers are 30 miles apart, with Station B directly south of Station A. Both stations saw a fire on the mountain to the south. The direction from Station A to the fire was N32 W. The direction from Station B to the fire was N40 ° E. How far (to the nearest mile) is Station B from the fire?

Answer 1

Let's make a diagram to represent the situation

The tower angle is found by using the interior angles theorem

`\begin{gathered} 50+58+T=180 \\ T=180-50-58=72 \end{gathered}`

It is important to know that the given directions are about the North axis, that's why we have to draw a line showing North to then find the interior angles on the base of the triangle formed.

To find the distance between the fire and Station B, we have to use the law of sines.

`(x)/(\sin58)=(30)/(\sin 72)`

Then, we solve for x

`\begin{gathered} x=(30\cdot\sin 58)/(\sin 72) \\ x\approx26.75 \end{gathered}`

Hence, Station B is 26.75 miles far away from the fire.