Question

two radar stations that are 25 miles apart and are both tracking a plane. At a given moment, the angle between station 1 and the plane is 73 degrees, the angle between station 2 and the plane is 46 degrees. What is the distance between the plane and station 2?

Answer 1

Use Law of Sines
180-73-46=61
sin61/25=sin73/x
x=25sin73/sin61= 27 mi
The distance between the plane and station 2 is 27 miles.

Answer 2

Let the station 1 as S1 and station 2 as S2. (please refer the diagram)

Distance between S1 and S2 = 25 miles

∠S2S1P = 73° and ∠S1S2P = 46°

So ∠S1PS2 = 180 - (73 +46) = 61°

According to the diagram, to find S2P we will use a sine law

$\frac{sin 73}{S2P} = \frac{sin 61}{S1S2} \\\\ \frac{0.9563}{S2P} = \frac{0.8746}{25}$

Cross multiply
$0.9563\times 25 = 0.8746 \times S2P\\\\ 23.9075 = 0.8746 \times S2P$

Divide both side by 0.8746
$\frac{23.9075}{0.8746} = S2P\\\\ S2P= 27.33$

So distance between the plane and station 2 is 27.33 miles