# Trig class - bearing problem

• Mar 30th 2009, 07:13 PM
Romanka
Trig class - bearing problem
Please, help me to solve the problem:
Two fire towers are located 85 km apart on hills A and B. The bearing from A to B is north east. A fire F is observed from tower A at N10E and from B at N75W. The town at point C is on bearing of N25E from A and S70W from B. The observers report the wind is blowing the fire directly toward C at a rate 9km/h. How many hours do the officials have to evacuate the town?

I can't find the distance FC(Crying)
Thank you.
• Mar 31st 2009, 08:07 AM
earboth
Quote:

Originally Posted by Romanka
Please, help me to solve the problem:
Two fire towers are located 85 km apart on hills A and B. The bearing from A to B is north east. A fire F is observed from tower A at N10E and from B at N75W. The town at point C is on bearing of N25E from A and S70W from B. The observers report the wind is blowing the fire directly toward C at a rate 9km/h. How many hours do the officials have to evacuate the town?

I can't find the distance FC(Crying)
Thank you.

I've attached a sketch.

1. Calculate all side lengthes of the triangle ABF (marked red)

2. Calculate all side lengthes in triangle ABC (marked blue)

3. Calculate the side length FC in triangle ACF.

• Mar 31st 2009, 08:31 AM
Romanka
I don't understand how to get angels in ABC (Itwasntme). I know how to find <C=135, but what about <A and <B?
And THANK YOU!!!
• Mar 31st 2009, 12:35 PM
earboth
Quote:

Originally Posted by Romanka
I don't understand how to get angels in ABC (Itwasntme). I know how to find <C=135, but what about <A and <B?
And THANK YOU!!!

Complete my sketch by adding the given angles. Then you can calculate the interior angles in the two triangles in question.
• Mar 31st 2009, 02:49 PM
Romanka
Sorry, I'm completely stupid (Crying), but
how to get the angles <A =20 and <B=25? It can be easily proved that their sum is 45 degrees... Why aren't they 22 and 23 degrees, or 18 and 27, for example?(Thinking)
If I could catch about angles then I can find everything for the problem.
Thank you!
• Mar 31st 2009, 11:44 PM
earboth
Quote:

Originally Posted by Romanka
Sorry, I'm completely stupid (Crying), but
how to get the angles <A =20 and <B=25? It can be easily proved that their sum is 45 degrees... Why aren't they 22 and 23 degrees, or 18 and 27, for example?(Thinking)
If I could catch about angles then I can find everything for the problem.
Thank you!

According to your question the line AB and the North direction include an angle of 45° = NE.

According to your question the line AC and the North direction include an angle of 25°.

Therefore the angle at A is 45° - 25° = 20°

You'll get the interior angle at B in a similar way:

The line BC and South include an angle of 70°.
The line BA and South include anangle of 45°.

Therefore the $\angle(CBA) = 70^\circ - 45^\circ = 25^\circ$

etc + andsoon (Thinking)
• Apr 1st 2009, 05:21 AM
Romanka
Quote:

Originally Posted by earboth
According to your question the line AB and the North direction include an angle of 45° = NE.

According to your question the line AC and the North direction include an angle of 25°.

etc + andsoon (Thinking)

(Blush) that's exactly what I missed!
Thank you so much!