Towers A and B are located 10 miles apart. A ranger spots a fire at a 42-degree angle from tower A. Another fire ranger spots the same fire at a 64-degree angle from tower B. To the nearest tenth of a mile how far from tower B is the fire?
7.0
7.4
9.4
13.4

The distance between tower B and the fire is  which agrees with the third option listed among the list of  possible answers.

Step-by-step explanation:

In order to understand which are our known elements of the triangle, we represent the quantities given in the diagram (please see attached image).

We understand that we can solve for the third angle in the triangle (the one defined by the vertex where the fire is by using:

Now that we know all angles, we can use a proportion from the law of sines to find side "x" which is the distance between the fire and tower B:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°