a 3ft tall boy casts a 4ft shawdow at the same time a tree casts a 72 foot shawdow using the pythagorean therem find the distance from the top of the tree to the tip of the shawdow
the Pythagorean Theorem is not what you need here.
The boy is 3/4 as tall as his shadow.
The tree is 3/4 as tall as its shadow.
so, what's 3/4 of 72?
You could use the theorem to find the distance from the boy's head to the tip of his shadow (d^2 = 3^2 + 4^2)
but that still wouldn't help you find the height of the tree. You'd still have to fall back on using similar triangles.
approximate to the nearest inch the lenght of a rectangle whose diagnol measures 25.0 inches and whose width is 18.0
Now you can use your theorem:
If the length is x, then
x^2 + 18^2 = 25^2
x^2 = 625 - 324
x^2 = 301
x = 17
a ladder 39 ft long leans against a building and reaches the ledge of a window if the foot of the ladder is 15 ft from the foot of the building how high is the window ledge above the ground tot the nearest foot.
come on. this is just like the one I just did for you. show me whatcha got. I'll let you know whether anything's amiss.
To find the distance from the top of the tree to the tip of the shadow, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two legs (sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this scenario, the height of the tree forms one leg of the right triangle, the length of its shadow forms the other leg, and the distance from the top of the tree to the tip of the shadow forms the hypotenuse.
Let's denote the height of the tree as 'x'. We know that the height of the boy is 3ft and his shadow is 4ft. Since both the boy and the tree are casting shadows at the same time, we can create a proportion:
(height of boy) : (length of boy's shadow) :: (height of tree) : (length of tree's shadow)
Using these values:
3ft : 4ft :: x : 72ft
To find 'x', we can cross-multiply:
3ft * 72ft = 4ft * x
216ft = 4ft * x
Dividing both sides by 4ft:
x = 216ft / 4ft
x = 54ft
Therefore, the distance from the top of the tree to the tip of the shadow is 54 feet.