The bearing of the fire from station A is N 60 degrees east. The bearing of the fire from station B is North 40 degreese west. How far is it from station a to the the fire?
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.
March 2nd, 2010 at 8:46 am
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
March 2nd, 2010 at 9:12 am
15.6 m
References :
March 2nd, 2010 at 9:28 am
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 :