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salem
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#1
Report Thread starter 16 years ago
#1
Hi!

I have the following question which I have failed to solve:

Three towns A, B and C lie on a straight road running east from A. B is 6 km from A and C is 22 km from A. Another town D lies to the north of this road and it lies 10 km from both B abd C. Calculate the distance of D from A and the bearing of D from A. :cool:
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way2go
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#2
Report 16 years ago
#2
(Original post by salem)
Hi!

I have the following question which I have failed to solve:

Three towns A, B and C lie on a straight road running east from A. B is 6 km from A and C is 22 km from A. Another town D lies to the north of this road and it lies 10 km from both B abd C. Calculate the distance of D from A and the bearing of D from A. :cool:
Just draw a picture and you find:

AD = sqrt(14^2+6^2)=sqrt(232)

I am not sure what you mean by bearing.
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elpaw
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#3
Report 16 years ago
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(Original post by way2go)
Just draw a picture and you find:

AD = sqrt(14^2+6^2)=sqrt(232)

I am not sure what you mean by bearing.
bearing is the angle from north.
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gzftan
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Report 16 years ago
#4
(Original post by salem)
Hi!

I have the following question which I have failed to solve:

Three towns A, B and C lie on a straight road running east from A. B is 6 km from A and C is 22 km from A. Another town D lies to the north of this road and it lies 10 km from both B abd C. Calculate the distance of D from A and the bearing of D from A. :cool:
try using pythagaros' theourum instead of trig...

G
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hornblower
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#5
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#5
(Original post by salem)
Hi!

I have the following question which I have failed to solve:

Three towns A, B and C lie on a straight road running east from A. B is 6 km from A and C is 22 km from A. Another town D lies to the north of this road and it lies 10 km from both B abd C. Calculate the distance of D from A and the bearing of D from A. :cool:

Sorry not to spoonfeed you but have you tried drawing a little sketch? Here are a couple of hints:

Triangle BCD is isosceles.
Make sure you know the cosine rule.


J.
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meepmeep
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Report 16 years ago
#6
(Original post by salem)
Hi!

I have the following question which I have failed to solve:

Three towns A, B and C lie on a straight road running east from A. B is 6 km from A and C is 22 km from A. Another town D lies to the north of this road and it lies 10 km from both B abd C. Calculate the distance of D from A and the bearing of D from A. :cool:
First thing to do is construct a diagram of the problem.

A, B and C should be on a straight line. Since D is the same distance from B and C this should tell you that BCD is an isosceles triangle. It will also be helpful to split this triangle down the middle so you get a right angled triangle. You can then use Pythagoras' theorem to find the length of AD. From this, you can get the bearing.

Good luck
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