SOLUTION: A dog on a leash is tied to the corner of a yard is 10 feet by 8 feet. If the leash is 12 feet long, how much area can the dog access. Please help me with word question.

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Question 1194039: A dog on a leash is tied to the corner of a yard is 10 feet by 8 feet. If the leash is 12 feet long, how much area can the dog access.
Please help me with word question.
Found 3 solutions by Edwin McCravy, ikleyn, ankor@dixie-net.com:
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
A dog on a leash is tied to the corner of a yard is 10 feet by 8 feet.
If the leash is 12 feet long, how much area can the dog access.
:
Draw this out, find the diagonal of the yard: d = = 12.8ft
The leash is only 12ft, so there will be small area above an arc where the dog cannot reach
:
Divide the dog access area into 3 sections, 2 right triangles and a portion of a circle.
Both triangles have a hypotenuse of 12, find the 3rd side of each triangle
Triangle 1:
s =
s = 8.94 ft
find the area
A1 = *8.94*8
A1 = 35.78 sq/ft
:
Triangle 2
s =
s = 6.63 ft
A2 = *10*6.63
A2 = 33.17 sq/ft
:
If we find the associated angles of these triangles, we can find the angle of the portion the circle for the 3rd area
Find the angle of the 1st triangle
Cos(a1) =
a1 = 48.2 degrees
Find the angle of the 2nd triangle
Cos(a2) =
a2 = 35.56 degrees
Find the angle of the arc in the circle
-----------------math error here!!!-------------------
90 - 48.2 - 35.5 = 6.3 degrees
Find the area of the portion of the circle we're interested in
A3 = *
A3 = 7.9 sq/ft
:
Find the total area the dog can roam
35.78 + 33.17 + 7.9 = 76.7 sq/ft
----------------I'm sorry!!!!-------------