Exercise 39 Page 820

Three tornado sirens $A,$ $B,$ and $C$ form a triangular region in one area of a city. We want to find the distance between sirens $B$ and $C .$ Let's consider the described situation on a diagram. We will call the missing distance $a .$

The side which length we want to find is situated opposite to the angle measuring

11 2^{\circ} .

We are given the distance between sirens

A

and

B

but we do not know the measure of the angle formed at Siren

C .

Let's use the Triangle Angle Sum Theorem to find its measure. It tells us that the sum of angle measures in a triangle is

18 0^{\circ} .

m ∠ C + 4 0^{\circ} + 11 2^{\circ} = 18 0^{\circ} \Rightarrow m ∠ C = 2 8^{\circ}

Let's add the obtained information to our diagram.

Since we now know the measure of two angles and the length of the side opposite to one of them, we can use the Law of Sines to find the value of $a .$