How tall is that tree? Walk 10 m back. Measure the angle from your eye to the top of the tree. Tangent does the rest.
Why tangent measures height
In the right triangle from your eye to the base of the tree to its top, the opposite side is the height above eye level and the adjacent side is your distance back. tan(angle) = opposite / adjacent, so opposite = distance × tan(angle). Add your eye-height and you've got the tree.
You stand 20 m from a flagpole and the angle to its top is 40°. Your eye is 1.5 m off the ground. How tall is the pole?
Stand at a distance roughly equal to the height you expect — that puts the angle near 45°, where small sighting errors matter least.
d = horizontal distance, θ = angle from horizontal
10 m back, angle 35°, eye 1.6 m up
h = 10 × tan(35°) + 1.6 ≈ 10 × 0.700 + 1.6 = 8.6 m.
A protractor + a drinking straw + a weight on a string = a working clinometer. Schools have built these for a hundred years.