Finding the Ratio of Angles of Tree A & B

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Homework Help Overview

The problem involves calculating the ratio of angles at which a person must look to view the tops of two trees of different heights from a specific distance. The context is rooted in trigonometry, specifically the use of tangent functions to determine angles based on height and distance.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of angles using the tangent function and question the method for finding the ratio of these angles. There is an exploration of the relationship between the height of the trees, the distance from the trees, and the resulting angles.

Discussion Status

The discussion includes attempts to clarify the calculation of angles and the ratio of these angles. Some participants confirm the approach while others seek validation of the reasonableness of the calculated angles. There is an acknowledgment of the method used to derive the angles from the triangle formed by the height and distance.

Contextual Notes

Participants are working under the constraints of a homework problem, which may limit the information available for discussion. The original poster expresses uncertainty about the correct method for calculating the ratio of angles.

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Homework Statement



Tree A is 10 m tall. Tree B is 60 m tall. You're standing on level ground at a position that is 25 m from tree A and 75 m from tree B. You're eye height is 1.5 m above the ground. Find the ratio of theta B/ theta A, of the angles (measured from the horizontal) at which you must look to view the top of each tree.



Homework Equations



tan(theta) tan -1 (theta)



The Attempt at a Solution



I think I have found both angles A and B: A = 18.8 degrees B = 37.95 degrees

This is absolutely crazy that I don't know how to find the B/A ratio! do I just put 37.95/18.8? Or do I need to divide both of them by 90 first, since the overall angle is a horizontal?

Thanks in advance.
 
Last edited:
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"B/A ratio"

It's just as you have shown B divided by A. i.e. 37.95/18.8 (note I didn't check you math for these angles)
 
thank you! do these angles sound reasonable?
 
How did you get these angles? What is the relation between the height of the tree, the distance from the tree and the angle?
 
With everything I knew I was able to form two triangles and in each I knew two sides. A: 8.5 and 25 and hypotenuse unknown. B: 58.5 and 75 and hypotenuse unknown. Using the tangent inverse, I found theta for each.
 
You got it. Good job.
 
Thank you =]
 

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