Solve for Tree Height: tan45=h/22

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Homework Help Overview

The problem involves calculating the height of a tree using trigonometric relationships, specifically focusing on the tangent of angles in right triangles.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of tangent and sine functions to relate angles and distances to the height of the tree. There is an exploration of different triangle setups and the relationships between various segments of the tree's height.

Discussion Status

Some participants have provided calculations and interpretations of the problem, while others have suggested reconsidering the definitions and relationships involved in the setup. There appears to be a mix of approaches being explored without a clear consensus on a single method.

Contextual Notes

Participants mention the need to clarify the definitions of different heights (h1 and h2) and the distances involved, indicating potential assumptions that may need to be addressed for a complete understanding of the problem.

chawki
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Homework Statement


see attachments.

Homework Equations


what is the height of the tree?

The Attempt at a Solution


It seems that tan45=h/22
h=22*tan45
h=22m
 

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  • tree.JPEG
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chawki said:
It seems that tan45=h/22

No. You need to look at right triangles. tan45o=h/d where d is the perpendicular distance from the endpoint to the tree.
By the way, you might want to call the top end of the tree height h1 and the bottom end h2 such that h1+h2=h (the total height of the tree).
 
like that ?

sin17=x/22
x=6.432m

tan28=z/y----(1)
we search y.
222= x2+y2
y2=222-x2
y2=484-41.37
y=21.038m

(1) <=> z=y*tan28 = 21.038*tan28 = 11.186m

height of tree = x+z = 6.432+11.186 = 17.618m
 

Attachments

  • tree.JPEG
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chawki said:
like that ?

sin17=x/22
x=6.432m

tan28=z/y----(1)
we search y.
222= x2+y2
y2=222-x2
y2=484-41.37
y=21.038m

(1) <=> z=y*tan28 = 21.038*tan28 = 11.186m

height of tree = x+z = 6.432+11.186 = 17.618m

Looks ok to me.
 

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