Friday

August 22, 2014

August 22, 2014

Posted by **Nikki** on Saturday, November 26, 2011 at 1:12am.

- Math -
**Steve**, Saturday, November 26, 2011 at 5:02amNot enough information.

Let the fire be at point F.

If the angle at P were 36.9 degrees, then we would have a right triangle with legs 15 and 20, and hypotenuse PF = 25.

However, since angle P is less than 36.9 degrees, a circle of radius 15 will cut the line PF extended in two places, either one of which would be a solution. The angle at F could be either acute or obtuse.

However, using the law of sines,

15/sin15° = 35.5 = 20/sinF

sinF = 20/35.5

F = 34° or 146°

PF/sin(180-(25+34)) = 35.5 makes PF = 30.42

PF/sin(180-(25+146)) = 35.5 makes PF = 5.38

SO, the distance PF depends on which direction the ranger was looking when he saw the fire.

**Related Questions**

Trig-sine, cosine law - Two fire stations,P and Q,are 20 km apart. A ranger at ...

math - a fire is sighted from two ranger stations that are 6000 meters apart. ...

Pre-Calc - Two lookout towers on Mount Abraham and Snow Mountain are 29 miles ...

Math - A forest ranger in a 140-foot observation tower sees a fire moving in a ...

Pre Calc - From an observation point A, a forest ranger sights a fire in the ...

Principles of Math 11 - A ranger in fire tower A spots a fire at a bearingof 295...

Geometry Part 2 - A forest ranger spots a fire from a 28- foot tower.The angle ...

Algebra - A ranger spots a forest fire while on a 45-meter observation tower. ...

5th Grade Math Problem - I posted this a little while ago, but didn't see it. ...

Trig word problem - A park ranger at point A sights a redwood tree at point B ...