Question

A boy stands inside a shadow cast by a tree, as shown in the diagram below.

A large right triangle is formed by the shadow and a perpendicular line from its hypotenuse to the base forms a small right triangle. Tree is at the height of the large right triangle and the boy is at the height of the small right triangle.

The boy knows his own height and can measure the length of his shadow as well as the length of the tree's shadow. Which postulate will allow the boy to find the height of the tree?

A.
SSS

B.
AA

C.
SAS

D.
AAS

Answer 1

B. AA

The two triangles (tree + its shadow, boy + his shadow) are right triangles and they share the same acute angle (direction of the sun rays). So by AA they are similar. Hence corresponding sides are proportional:

tree height / boy height = tree shadow / boy shadow,

so tree height = boy height × (tree shadow / boy shadow).