Comments on: Two fire look out stations are 20 miles apart with station B east of station A. Both station spot a fire? http://www.wegafire.com/fire-station/two-fire-look-out-stations-are-20-miles-apart-with-station-b-east-of-station-a-both-station-spot-a-fire Thu, 02 Feb 2012 06:34:59 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Kim http://www.wegafire.com/fire-station/two-fire-look-out-stations-are-20-miles-apart-with-station-b-east-of-station-a-both-station-spot-a-fire/comment-page-1#comment-2070 Kim Tue, 02 Mar 2010 14:28:59 +0000 http://www.wegafire.com/fire-station/two-fire-look-out-stations-are-20-miles-apart-with-station-b-east-of-station-a-both-station-spot-a-fire#comment-2070 N 60° E means "60° east of north" N 40° W means "40° west of north" It helps if you draw a triangle. If you draw vertical lines on either side of the triangle, you can see that the exterior angle of A is 60 degrees, so the inner angle must be 30. The exterior angle of angle B is 40, so the inner angle is 50 degrees. All the interior angles add up to 180 degrees, so angle C is 100 degrees. A = 30 degrees B= 50 degrees C = 100 degrees a = ? b = ? c = 20 miles Now you can use the Rule of Sines to solve the rest. a/sinA = b/sinB = c/sinC b/sinB = 20/sin100 b = (20sin50)/sin100 b is about 15.57 miles Using the same rule, a was about 10.2 miles. Anyway the answer was 15.57 miles rounded up to 16.<br><b>References : </b><br> N 60° E means "60° east of north"
N 40° W means "40° west of north"

It helps if you draw a triangle.

If you draw vertical lines on either side of the triangle, you can see that the exterior angle of A is 60 degrees, so the inner angle must be 30.

The exterior angle of angle B is 40, so the inner angle is 50 degrees.

All the interior angles add up to 180 degrees, so angle C is 100 degrees.

A = 30 degrees
B= 50 degrees
C = 100 degrees
a = ?
b = ?
c = 20 miles

Now you can use the Rule of Sines to solve the rest.

a/sinA = b/sinB = c/sinC

b/sinB = 20/sin100

b = (20sin50)/sin100

b is about 15.57 miles

Using the same rule, a was about 10.2 miles.

Anyway the answer was 15.57 miles rounded up to 16.
References :

]]> By: Dilon http://www.wegafire.com/fire-station/two-fire-look-out-stations-are-20-miles-apart-with-station-b-east-of-station-a-both-station-spot-a-fire/comment-page-1#comment-2069 Dilon Tue, 02 Mar 2010 14:12:59 +0000 http://www.wegafire.com/fire-station/two-fire-look-out-stations-are-20-miles-apart-with-station-b-east-of-station-a-both-station-spot-a-fire#comment-2069 15.6 m<br><b>References : </b><br> 15.6 m
References :

]]> By: Rik D http://www.wegafire.com/fire-station/two-fire-look-out-stations-are-20-miles-apart-with-station-b-east-of-station-a-both-station-spot-a-fire/comment-page-1#comment-2068 Rik D Tue, 02 Mar 2010 13:46:59 +0000 http://www.wegafire.com/fire-station/two-fire-look-out-stations-are-20-miles-apart-with-station-b-east-of-station-a-both-station-spot-a-fire#comment-2068 N 60° E means "60° east of north" N 40° W means "40° west of north" d = sqrt( f^2 + h^2 ) tan 30° = h/f => f = h / tan 30° tan 50° = h / g => g = h / tan 50° f + g = [h / tan 30°] + [h / tan 50°] = 20 => (1 / tan 30° + 1 / tan 50° )h = 20 => h = 20 / (1 / tan 30° + 1 / tan 50° ) = 7.77861913 mi => f = 7.77861913 / tan 30° = 13.4729635 mi => d = sqrt( 13.4729635^2 + 7.77861913^2 ) = 15.5572382 mi ˜ 15.6 mi<br><b>References : </b><br>Googled it N 60° E means "60° east of north"
N 40° W means "40° west of north"

d = sqrt( f^2 + h^2 )

tan 30° = h/f =>

f = h / tan 30°

tan 50° = h / g =>

g = h / tan 50°

f + g = [h / tan 30°] + [h / tan 50°] = 20 =>

(1 / tan 30° + 1 / tan 50° )h = 20 =>

h = 20 / (1 / tan 30° + 1 / tan 50° )

= 7.77861913 mi =>

f = 7.77861913 / tan 30°

= 13.4729635 mi =>

d = sqrt( 13.4729635^2 + 7.77861913^2 )

= 15.5572382 mi

˜ 15.6 mi
References :
Googled it

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