A forest fire is spotted from two fire towers. the triangle determined by two towers and the fire has angles of 28 degrees and 37 degrees at the tower vertices. If the towers are 3000 meters apart, which one is closer to the fire.

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- May 26th 2008, 07:07 PMvictorfk06Triangle Problem with sines
A forest fire is spotted from two fire towers. the triangle determined by two towers and the fire has angles of 28 degrees and 37 degrees at the tower vertices. If the towers are 3000 meters apart, which one is closer to the fire.

- May 26th 2008, 09:58 PMearboth
1. Draw a sketch

2. The angle at the fire tower is 115°.

3. Use Sine Rule:

$\displaystyle \frac{x}{3000}=\frac{\sin(37^\circ)}{\sin(115^\cir c)}$

$\displaystyle \frac{y}{3000}=\frac{\sin(28^\circ)}{\sin(115^\cir c)}$

4. Without any calculations it is obvious that y < x because sin(28°) < sin(37°)