Question

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 mi 7.4 mi 9.4 mi 13.4 mi

Answer 1

Answer:

9.4

Step-by-step explanation:

We are solving for b, not a. I know this because I did this problem before and it has popped up here again on brainly. That is why the guest commented "it is incorrect'

Answer 2

Answer:

7.0 mi

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

$A+B+C=180^o$

substitute the given values

$42^o+64^o+C=180^o$

$C=180^o-106^o=74^o$

step 2

Find the measure of a

Applying the law of sines

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

substitute the given values

$\frac{10}{sin(74^o)}=\frac{a}{sin(42^o)}$

solve for a

$a=\frac{10}{sin(74^o)}sin(42^o)$

$a=7.0\ mi$