Question

Mark is interested in measuring the height of a tree in his yard. He measures the length of the tree’s shadow at 16 feet. At the same time, his own shadow is 2 feet 8 inches. If Mark is 6’10”, how tall is the tree?

Answer 1

Solution:

According to question
Mark is interested in measuring the height of a tree in his yard. He measures the length of the tree’s shadow at 16 feet. At the same time, his own shadow is 2 feet 8 inches. If Mark is 6’10.Then length of tree is

By using ratio

Mark height : Mark shadow height .... (1)

Tree height : tree shadow height ... (2)

Mark height / Mark shadow height = Tree height /Tree shadow height

= 6 ft 10 inches / 2 ft 8 inches = Tree height / 16 ft

Let tree height be T

= 6ft 10inches * 16ft /2ft 8 inches = T ( 6ft 10 inches = 6+10/12 ft)

=(6 +10/12 )*16 /(2 +8/12) = T

= 6.833 * 16 / 2.666

= 109.328/2.666 = 41.008 ft = Tree height