Sunday

April 20, 2014

April 20, 2014

Posted by **Billy Bob** on Tuesday, May 22, 2012 at 6:41pm.

two forest fire towers, A and B are 20.3km apart. From tower A, the bearing of tower B is 70 degrees. The ranger in each tower observes a fire and radios the bearing from the tower. the bearing from tower A is 25 degrees and from tower B is 345 degrees. How far, to the nearest tenth of a kilometre is the fire from each tower?

the other questions is:

The interior angles of a triangle are 120 degrees, 40 degrees, and 20 degrees. The longest side is 10cm longer than the shortest side. Determine the perimeter of the triangle to the nearest centimetre.

Thanks

- Grade 11 Math -
**Reiny**, Tuesday, May 22, 2012 at 8:01pmNever attempt a question like this without a sketch or diagram.

I labeled the position of the fire as F

and by some simple adding/subtracting of angles, I had angle A = 45° and angle B = 95°, thus angle F = 40° , and AB = 20.3

By sine law:

AF/sin95 = 20.3/sin40

AF = 20.3sin95/sin40 = appr31.46 km

BF/sin45 = 20.3/sin40

.....

the second one is quite easy,

make a sketch of the triangle, place x as the side opposite the 20° angle and (x+10) opposite the 120° angle.

by sine law :

x/sin20 = (x+10)/sin120

xsin120 = xsin20 + 10sin20

xsin120 - xsin20 = 10sin20

x(sin120 - sin20) = 10sin20

x = 10sin20/(sin120-sin20) = appr 6.527

so the smallest side is 6.527,

the largest side is 16.527

Use the sine law once more to find the third side, then add up the 3 sides.

**Related Questions**

Math - two forest fire stations,P and Q are 20.0 km apart, A ranger at station Q...

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

algebra - if the damage caused by forest fire A is measured in shape of a ...

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

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

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

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

Environmental Science - What kind of natural disasters help some forest ...

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

English - I forgot to include the following sentences. Thank you. 1) A volunteer...