A student is 5 ft tall and casts a shadow 10 ft long. A nearby tree casts a shadow 60 ft long. Find the height h of the tree.
draw a diagram. Using similar triangles,
h/60 = 5/10
To find the height of the tree (h), we can set up a proportion using similar triangles.
Let's represent the height of the student as s, the length of the student's shadow as x, the height of the tree as h, and the length of the tree's shadow as y.
According to the given information, the student's height (s) is 5 ft, and the length of their shadow (x) is 10 ft. The tree's shadow (y) is 60 ft.
We can set up the proportion as follows:
s / x = h / y
Substitute the given values into the proportion:
5 / 10 = h / 60
Simplify the proportion:
1/2 = h / 60
To solve for h, we can cross-multiply:
Cross-multiplying gives us:
2h = 1 * 60
2h = 60
Divide both sides of the equation by 2 to isolate h:
h = 60 / 2
h = 30
Therefore, the height of the tree is 30 ft.