Posted by **Nada** on Tuesday, July 20, 2010 at 7:55pm.

Two fire stations,P and Q,are 20 km apart. A ranger at station Q sees a fire 15.0 km away. If the angle between the line PQ and the line from P to the fire is 25degrees, how far to the nearest tenth of a kilometre, is station P from the fire?

- Trig-sine, cosine law -
**Reiny**, Tuesday, July 20, 2010 at 8:00pm
Now this one is easy to see and draw.

direct application of cosine law,

x^2 = 20^2 + 15^2 - 2(20)(15)cos 25°

= 81.21533

x = 9.01 km

- Trig-sine, cosine law -
**Nada**, Tuesday, July 20, 2010 at 8:05pm
Um the answer I was given was 5.7km or 30.5km

So how wud u get these answers?

- Trig-sine, cosine law -
**Reiny**, Tuesday, July 20, 2010 at 9:54pm
Yup, I made a mistake, I didn't mind my P's and Q's

I now have the fire at F, and PQ=20, FQ=15 and angle QPF=25°

so we have the ambiguous case of the sine law.

let PF = x

first we have to find angle F

sinF/20 = sin25/15

sinF = .5635

angle F = 34.3° , then angle Q = 120.7

or angle F = 145.7°, then angle Q = 9.3°

case 1:

x/sin 9.3 = 15/sin25

x = 5.73

case 2

x/sin120.7 = 15/sin25

x = 30.52

x =

- Trig-sine, cosine law -
**Nada**, Tuesday, July 20, 2010 at 10:03pm
Thank you so much:)

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