Hello, wanderlust!

An air traffic patrol helicopter hovering at $\displaystyle C$ sights a vehicle at $\displaystyle A.$

One minute later the vehicle is at $\displaystyle B.$

Find the speed of the vehicle in miles per hour. Code:

- - - - - - - - - - - o C
37° * *|
*35°* |
* * |
* *18°|
* * | 3000
* * |
* * |
* * |
* 37° 108° * 72° |
o - - - - - - - - - o - - - - *
B x A D

Let: $\displaystyle x = AB$

We can determine *all* the angle in the problem.

. . (I hope you followed that.)

In right triangle $\displaystyle CDA\!:\;\;\sin72^o \,=\,\frac{3000}{AC} \quad\Rightarrow\quad AC \:=\:\frac{3000}{\sin72^o} \:\approx\:3154.4 $

In $\displaystyle \Delta CAB\text{, the Law of Sines: }\;\frac{x}{\sin35^o} \:=\:\frac{AC}{\sin37^o} \quad\Rightarrow\quad x \:=\:\frac{3154.4\,\sin35^o}{\sin37^o} \:\approx\:3006.4$

Hence, the card drove 3006.4 feet in one minute.

That's 180,384 feet in one hour,

. . or about 34.2 miles in one hour.

The speed of the car is 34.2 mph.