Question

A tree outside Ellie's house casts a 125-foot shadow. At the same time of the day, Ellie casts a 5.5-foot shadow. If Ellie is 4 feet 10 inches tall, how tall is the tree in feet?

Answer 1

Answer:

The tall of the tree is about 109.85 feet

Step-by-step explanation:

* Lets study the situation in the problem

- The tree and its shadow formed a right angle triangle with legs

  x the tall of the tree and 125 feet the shadow of the tree

- Ellie and her shadow formed a right triangle with legs 4 feet and

 10 inches the tall of Ellie and 5.5 feet the shadow of Ellie

- The two triangles are similar

- There is an equal ratio between the corresponding sides of the

 similar triangles

# Ex: If triangles ABC and XYZ are similar

∴ AB/XY = BC/YZ = AC/XZ

* Lets use this rule to solve the problem

∵ The tall of the tree is x

∵ The tall of Ellie is 4 feet and 10 inches

- Lets change the tall of Ellie to feet only

∵ 1 foot = 12 inches

∴ 10 inches = 10/12 = 5/6 foot

∴ The tall of Ellie is 4 feet and 5/6 foot = 4 + 5/6 = 29/6 feet

∵ The shadow of the tree is 125 feet

∵ The shadow of Ellie is 5.5 feet

- By using similarity ratio

∴ Tall of tree/tall of Ellie = shadow of tree/shadow of Ellie

∴ x/(29/6) = 125/5.5 ⇒ using cross multiplication

∴ 5.5(x) = 125(29/6) ⇒ divide both sides by 5.5

∴ x ≅ 109.85 feet

* The tall of the tree is about 109.85 feet