SOLUTION: Use similar triangles to solve. A person who its 5 feet tall is standing 143 feet from the base of a tree, and the tree casts a 154 foot shadow. The persons shadow is 11feet in len
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Question 631101: Use similar triangles to solve. A person who its 5 feet tall is standing 143 feet from the base of a tree, and the tree casts a 154 foot shadow. The persons shadow is 11feet in length. What is the height of the tree? Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! We can think of all the rays of sun as parallel lines.
We can think of the person and the tree as vertical line segments.
We can think of the ground as a perfectly flat horizontal plane.
The person, the person's shadow, and the sun ray from the top of the person's head to the top of the shadow from a right triangle.
The tree, its shadow, and the sun ray from the top of the tree to the tip of its shadow also form a right triangle.
Those two triangles are similar to each other because the angles of the sun rays with the ground are congruent.
Sun rays are red, tree is green, person is the short blue line next to the 5.
The triangles are similar because their angles are congruent (same measures).
corresponding sides are in the same ratio.
The small triangle is a scaled down version of the large one. --> -->
By the way, the fact that the person was standing 143 feet from the tree is irrelevant. That number was thrown in there to see if you really understood the situation. In my drawing, I put the person at 170 feet from the foot of the tree to make the drawing readable. Otherwise the two triangles would look jumbled together).
