silemus.
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  1. 9Similar triangles, shadows
  2. 10Similar triangles, area ratio
  3. 1230-60-90 triangle sides
  4. 14Angle of elevation, right triangle
  5. 18Inscribed angle theorem
  6. 19Angle in a semicircle
  7. 21Equal tangent lengths
  8. 22Chord distance from centre
  9. 26Interior angles of an octagon
  10. 30Area and side of a rhombus
  11. 31Prism volume and surface area
  12. 33Volume and slant height of cone
  13. 40Perpendicular bisector
  14. 41Area of triangle by coords
  15. 42Circle, completing the square

9Similar triangles, shadows

A person 1.8 m tall casts a shadow 2.4 m long. At the same time a tree casts a shadow 16 m long. How tall is the tree?

The tree is 12 m tall. Since the sun casts shadows at the same angle, the person's height-to-shadow ratio equals the tree's: 1.8/2.4 = h/16, giving h = 28.8/2.4 = 12 m.

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