Ratio of elevation angles to view tops of two trees

[chantalprince]

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.

 

[dlgoff]

"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)

 

[chantalprince]

thank you! do these angles sound reasonable?

 

[dlgoff]

How did you get these angles? What is the relation between the height of the tree, the distance from the tree and the angle?

 

[chantalprince]

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.

 

[dlgoff]

You got it. Good job.

 

[chantalprince]

Thank you =]