Question

A fierce guard dog is tethered by a 15 m chain to a post that is 6 m from a straight path. For what distance along the path is a trespasser in danger from the dog?​

Answer 1

The distance from the road where an intruder would be in danger is 27.48 m.

To know how far from the road an intruder is in danger due to the dog, it is necessary to carry out the following procedure:

Establish the range of the dog with a circle of 15 meters in radius around the post on which he is tied.

In this part it can be inferred that a part of the path is in the range of the dog between points B and D (In this area the intruder would be in danger)

From this we know the following data:

• Length AB = 15m
• Length AD = 15m
• Length AC = 6m

To know the length of points BC and CD we must perform a calculation using the formula of the Pythagorean theorem.

• BC = $\sqrt{15^{2} - 6^{2} }$
• BC = $\sqrt{225-36}$
• BC = $\sqrt{189}$
• BC = 13,74 m

Later we use the same procedure to find the length CD.

• CD = $\sqrt{15^{2} - 6^{2} }$
• CD = $\sqrt{225-36}$
• CD = $\sqrt{189}$
• CD = 13,74 m

Finally, we add both lengths (BC + CD) to know the distance in which an intruder is in danger within the dog's range.

• BC + CD = BD = 27,48 m

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