Question

Two weather stations are aware of a thunderstorm located at point C. The weather stations A and B are 27 miles apart. How far is weather station A from the storm

Answer 1

Station A is at a distance of 28.83 miles from the storm

Sine rule

Sine rule is used to show the relationship between the sides of a triangle as well as their opposite angles. It is given by:

$\frac{a}{sin(A)}= \frac{b}{sin(B)}=\frac{c}{sin(C)}$

From the diagram:

• A = 34° + 90° = 124°

Also:

• B = 90° - 61° = 29°

Hence:

• C + A + B = 180°
• C + 29 + 124 = 180
• C = 27°

b = distance station A from the storm, c = AB = 27 miles

Using sine rule:

$\frac{c}{sin(C)} =\frac{b}{sin(B)} \\\\\frac{27}{sin(27)}=\frac{b}{sin(29)} \\\\b=28.83\ miles$

Station A is at a distance of 28.83 miles from the storm