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two towers labeled Tower A and Tower B some distance apart and a fire image at a certain distance from both towers 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 A is the fire?

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calculista

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

[tex]A+B+C=180^o[/tex]

substitute the given values

[tex]42^o+64^o+C=180^o\\C=180^o-106^o=74^o[/tex]

step 2

Find the measure of a

Applying the law of sines

[tex]\frac{c}{sin(C)}=\frac{a}{sin(A)}[/tex]

substitute the given values

[tex]\frac{10}{sin(74^o)}=\frac{a}{sin(42^o)}[/tex]

solve for a

[tex]a=\frac{10}{sin(74^o)}sin(42^o)\\a=7.0\ mi[/tex]

Ver imagen calculista

Answer:

7.0 m

Step-by-step explanation:

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