SOLUTION: 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 i

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Question 301899: 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.
This is a homework question. I have serious problems with word questions dealing with any type of Math. That has always been my weak point. So I am asking for your help. If you can, thank you. I do appreciate any assistance you can give me.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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
=
Cross multiply
10.35t = 1.51*31.05
10.35t = 46.8855
t =
t = 4.53 m is the height of the tree
:
:
Did this make sense to you? Drawing a diagram of this can help.
Any questions about it?