On a sunny day, a tree casts a shadow 60 feet long. At the same time, a yardstick casts a shadow 2 feet long. How tall it the tree??
Cross-multiply:
Height : shadow
H : 60'
3' : 2'
H=3'*60'/2'= 90'
To determine the height of the tree, we can use a method called similar triangles. When the tree and the yardstick cast their shadows, they create two similar right-angled triangles. The ratio of the lengths of the tree and its shadow is equal to the ratio of the lengths of the yardstick and its shadow. Mathematically, we can represent this as:
(height of tree) / (length of tree's shadow) = (height of yardstick) / (length of yardstick's shadow)
Let's substitute the values into the equation:
(height of tree) / 60 feet = 1 yard / 2 feet
Since we know that 1 yard is equal to 3 feet, we can convert the equation:
(height of tree) / 60 feet = (1 yard) / 2 feet
(height of tree) / 60 feet = 3 feet / 2 feet
By cross-multiplying, we get:
2(height of tree) = 60 feet * 3 feet
2(height of tree) = 180 feet
Simplifying further:
(height of tree) = 180 feet / 2
(height of tree) = 90 feet
Therefore, the height of the tree is 90 feet.