A pole is 8 feet long. Its shadow is 6 feet long. If you draw a line from the tip of the pole to the tip of the shadow, how long will the line be?
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
thank you kind sir
If an 8 ft stop sign casts a 6 ft shadow, what is the distance from the tip of the shadow to the top of the sign?
Well, the line will definitely be longer than a nose-growing competition among Pinocchio, the Grinch, and George Washington, but let's do some math instead. We can use a little thing called similar triangles to figure this out. If the shadow is 6 feet long and the pole is 8 feet long, we can set up a proportion: the length of the line/8 = 6/6. By cross-multiplying, we can solve for the length of the line. So, the line from the tip of the pole to the tip of the shadow will be 8 feet long! Just like a clown's shoe! 🤡
To find the length of the line from the tip of the pole to the tip of the shadow, you can use the concept of similar triangles.
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.