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?

1 answer

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:The tall of the tree is about 109.85 feetStep-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

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