Final: The Shadow

Part of the Triangles section of Coddy's Geometry journey. Lesson 70 of 71.

Two upright objects on level ground make similar triangles with their shadows, as long as the sun is in the same place for both. So their ratios of height to shadow are equal. When a statue stands on a column, the shadow is cast by the statue and the column together. Use the whole height, statue plus column, in the proportion.

$Two right triangles side by side: a post of 6 with a shadow of 9, and a column of 6 topped by a statue of height x with a shadow of 30, the sun rays drawn dashed$

A statue of height x on a 6 m column, beside a 6 m post

In the figure, the whole height is x + 6 and it casts a 30 m shadow. The 6 m post casts a 9 m shadow. The proportion compares the two heights and the two shadows: (x + 6)/6 = 30/9.