Shortcut Trick
The ratio of heights of the pole and the tree is 18 : 6 = 3 : 1.
In similar triangles, the ratio of their total distance from the shadow tip to the shadow length must be the same: (10 + s) : s = 3 : 1.
Using the unitary method, if 3 parts = 10 + s and 1 part = s, then the difference (2 parts) = 10 feet.
Since 2 parts = 10 feet, then 1 part (shadow length s) = 10 ÷ 2 = 5 feet.
∴ The correct answer is 5 feet.
Alternate Method
Given: Height of electric pole (H) = 18 feet, Height of tree (h) = 6 feet, Distance between pole and tree (d) = 10 feet.
The light ray from the top of the pole passes the top of the tree to form the shadow, creating two similar triangles.
⇒ (Height of Pole) ÷ (Total Distance from Pole to Shadow Tip) = (Height of Tree) ÷ (Shadow Length)
⇒ 18 ÷ (10 + s) = 6 ÷ s
⇒ 18 × s = 6 × (10 + s)
⇒ 3s = 10 + s
⇒ 3s − s = 10
⇒ 2s = 10
⇒ s = 5 feet
∴ The correct answer is 5 feet.
Additional Information
Properties of Similar Triangles
Two triangles are similar if their corresponding angles are equal; their corresponding sides are always in the same ratio.
Shadow Length Formula
For objects sharing the same elevation angle of a light source: (Object Height1 / Shadow Length1) = (Object Height2 / Shadow Length2).
Thales Theorem
Also known as the Basic Proportionality Theorem, it states that a line drawn parallel to one side of a triangle divides the other two sides in the same ratio.