Yosief is 4 feet 9 inch boy. He stands in front of a tree and sees that it's shadow coincide with his. Yosief shadow measures 9 feet 6 inches. Yosief measures the distance between him and the tree to calculate its height, how does he do it?

Question

Aurora Ayala · Accepted Answer

Using the properties of similar triangle we can write #"height of the tree"/"height of the boy"="shadow of the tree"/"shadow of the boy"# #=>"height of the tree"/"4ft 9in"="20ft 6 in+9ft 6in"/"9ft 6in"# #=>"height of the tree"="30×12(4×12+9)"/"9×12+6 "# in #=>"height of the tree"="360×57"/"114 "# in=15ft

Evelyn Arboleda · Answer

undefined Yosief can use similar triangles to calculate the height of the tree. The ratio of his height to his shadow's height is the same as the ratio of the tree's height to its shadow's height.

Yosief's height: 4 feet 9 inches
Yosief's shadow: 9 feet 6 inches

Tree's shadow: 9 feet 6 inches

Using the ratios:

Yosief's height / Yosief's shadow = Tree's height / Tree's shadow

(4.75 feet) / (9.5 feet) = Tree's height / (9.5 feet)

Now, solve for the tree's height:

Tree's height = (4.75 feet / 9.5 feet) * (9.5 feet)

Tree's height = 4.75 feet