Question #a5b7f

1 Answer
Jarni Renz
Feb 2, 2018

#h=8m#

Explanation:

This can be solved through ratio and proportion. First assume variables to represent each measurement; i.e.,

Let:

#x="the shadow of the man"#

#y="the height of the tree"#

Since the #"height of the man"=2m# and its shadow is assumed as #x#; and the #"shadow of the tree is"= 4x "# longer than the shadow of the man"#(x)#, and its height is assumed as #y#. The ratio can be interpreted as

#2:x=y:4x#

These two references cast similar shadows since the rays of the sun are parallel to each other and the angle of hypotenuse formed are the same for both references. Note that similar triangles have the same shapes and angles; thus, the ratio can be set-up as shown below.

#2:x=y:4x# or

#2/x=y/(4x#; cancel same variable

#2/cancel(x)=y/(4cancel(x)#
#y=8m#

Therefore, the tree is #8m# tall.

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