SOLUTION: Matt is 1.59 m tall and wants to find the height of a tree. He walks 21.80 m from the base of the tree along the shadow until his head is in a position where the tip of his shadow

Algebra ->  Trigonometry-basics -> SOLUTION: Matt is 1.59 m tall and wants to find the height of a tree. He walks 21.80 m from the base of the tree along the shadow until his head is in a position where the tip of his shadow       Log On


   

Question 160063: Matt is 1.59 m tall and wants to find the height of a tree. He walks 21.80 m from the base of the tree along the shadow until his head is in a position where the tip of his shadow exactly overlaps the end of the tree top's shadow. He is now 5.99 m from the end of the shadows. How tall is the tree? Round to nearest hundredth. The answer should be 7.38m but I have no idea how to reach that answer. I am assuming I should set up a proportion but I am not sure. Can you help?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
Matt, the tree, and the shadows form similar triangles (you're right about the proportion)

Matt/Matt's shadow=tree/tree's shadow __ 1.59/5.99=t/(21.80+5.99)

1.59 * 27.79 / 5.99 = t