Question 302213
Julia, who is 1.51 m tall, wishes to find the height of a tree with a shadow 31.05 m long. 
She walks 20.70 m from the base of the tree along the shadow of the tree until 
her head is in a position where the tip of her shadow exactly overlaps the end of the tree top's shadow. 
How tall is the tree? Round to the nearest hundredth.
:
We can use the property of two similar triangles. Corresponding sides have same ratios.
:
the triangle formed by the tree, it's shadow, and line to the sun
is similar to:
 the triangle formed by the person, her shadow, and line to the sun
:
let t = height of the tree
tree shadow given as 31.05 m
;
person height = 1.51 m
person shadow: 31.05 - 20.70 = 10.35 m 
:
A simple ratio equation using corresponding sides of each triangle
tree height:person height = tree shadow:person shadow
{{{t/1.51}}} = {{{31.05/10.35}}}
Cross multiply
10.35t = 1.51*31.05
10.35t = 46.8855
t = {{{46.8855/10.35}}}
t = 4.53 m is the height of the tree
:
: