Question

lets say you have a tree or a flagpole. Describe how you would measure this object using right angled triganometry

Answer 1

stick a stick vertically in the ground.
measure the height and shadow of the stick.

measure the shadow of the tree, and use the same ratio to calculate its height.

extra credit: why does this work?

Answer 2

I think i have to use soh cah toa instead of similar triangles

Answer 3

unless you can measure the angle, you have to use similar triangles. If you can measure the angle sighting from the tip of the stick's shadow to the top of the stick, then

tanθ = opposite/adjacent

The same angle is made from the pole's shadow to the top of the pole.

So, if the shadow is length s, and the pole is height p, then

p/s = tanθ