# Angle Ratios

1. 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.

2. Homework Equations

tan(theta) tan -1 (theta)

3. 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?

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dlgoff
Gold Member
"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?

dlgoff
Gold Member
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.

dlgoff