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Late one afternoon, while being chased by the Sheriff of Nottingham into an unfamiliar part of Sherwood forest, Robin Hood and Little John found themselves trapped between a wide chasm and the approaching evil sheriff Fortunately, the sign from the old collapsed bridge was still standing, for it gave Robin the information necessary to plan his escape. The sign said the chasm was 36 feet across. A large tree grew near the chasm. It was the only tree within 50 yards of the chasm Robin quickly paced off the distance from the cliff edge to the tree and found that it was 18 feet. He noticed that the shadow cast by the tree stretched directly across the chasm and that the tip of the shadow just reached the opposite edge of the chasm . Robin hastily measured the shadow created by his 55-inch frame and found it to be 77 inches. Using this information , Rohin calculated the height of the tree. What was the height of the tree to the nearest foot?

Sagot :

The ratio of the height of the tree to the length of the shadow of the tree

is given by the ratio of the height of the frame to its shadow.

Response:

  • The height of the tree is approximately 39 feet

Which method can be used to calculate the height of the tree?

The given information are;

The distance from the tree to the other side of the chasm = 18 + 36 = 54

Length of the shadow cast by the tree = 54 feet

Height of the frame = 55-inch

Length of the shadow created by the frame = 77 inches

By similar triangles, have;

[tex]\dfrac{Height \ of \ frame}{Length \ of \ shadow \ created \ by \ frame} = \mathbf{\dfrac{Height \ of \ tree}{Length \ of \ shadow \ created \ by \ tree}}[/tex]

Which gives;

[tex]\dfrac{55}{77} = \mathbf{\dfrac{Height \ of \ tree}{54}}[/tex]

[tex]Height \ of \ tree = \dfrac{55}{77} \times {54} \approx \mathbf{39}[/tex]

  • The height of the tree is approximately 39 feet

Learn more about similar triangles here:

https://brainly.com/question/8242716

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