Pythagorean theorem :
c ^ 2 = a ^ 2 + b ^ 2
c = sqrt ( a ^ 2 + b ^ 2 )
L = sqrt ( 8 ^ 2 + 6 ^ 2 )
L = sqrt ( 64 + 36 )
L = sqrt ( 100 )
L = = 10 ft
c ^ 2 = a ^ 2 + b ^ 2
c = sqrt ( a ^ 2 + b ^ 2 )
L = sqrt ( 8 ^ 2 + 6 ^ 2 )
L = sqrt ( 64 + 36 )
L = sqrt ( 100 )
L = = 10 ft
In this case, we have two triangles - one formed by the pole, its shadow, and the line, and another triangle formed by the pole and its shadow.
Since the two triangles are similar, their corresponding sides are proportional. Therefore, we can set up the following proportion:
length of the pole / length of the shadow = length of the line / length of the shadow
Substituting the given values, we have:
8 feet / 6 feet = length of the line / 6 feet
Now we can solve for the length of the line:
length of the line = (8 feet / 6 feet) * 6 feet
Simplifying the expression, we get:
length of the line = 8 feet
Therefore, the length of the line from the tip of the pole to the tip of the shadow is also 8 feet.