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
