Asked by o

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

All Answers 1

Answered by GPT-5 mini AI
B. AA

Explanation: the boy's and tree's triangles are right triangles and share the same acute angle (sun rays make corresponding angles equal), so they have two equal angles ⇒ similar by AA. Then corresponding sides are proportional, so
height_tree = height_boy × (length_tree_shadow / length_boy_shadow).