Shadow Height Calculator

Pre-Algebra · Axiom Academy

LESSON Shadow Height Calculator How can you measure the height of a tree without climbing it? Use shadows and similar triangles. The sun is so far away that its rays arrive parallel — they strike a short stick and a tall tree at the exact same angle. Each object, its shadow, and the slanted ray form a right triangle . Watch both triangles draw in: they share that sun angle and they each have a right angle at the ground, so they are similar — identical in shape, different in size. 2. The Ratio Height ÷ Shadow Is Constant In similar triangles, matching sides are proportional . Here that means each object's height divided by its shadow gives the same number — it only depends on the sun's angle, not on how big the object is. The animation grows each triangle's height bar and shadow bar and shows both ratios landing on the same value. The ratio of height to shadow is the same for both objects. A 6 ft person casts an 8 ft shadow. Ratio of height to shadow: . The tree casts a 20 ft shadow. Its height is unknown — but its ratio must also be 0.75 . If the tree's ratio were different, its triangle would be a different shape — which can't happen when the same parallel sunlight hits both. Same angle forces the same ratio. 3. Set Up the Proportion and Solve

This is the written version of the interactive lesson above. See the full Pre-Algebra course.