Answer:
The height of the house is 30 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- Name the place of the mirror with M
- Name the place of Paul with P
∴ MP is the distance between Paul and the mirror
∵ The distance between Paul and the mirror is 5 feet
∴ MP = 5
- Name the place of Paul's eyes with E
- Name the tip of the roof with T
∴ MET is a line segment
- Name the place of the house on the ground with H
- The line TH represent the height of the house
∴ TH = the height of the house
- The line HM is the distance between the house and the mirror
∵ The distance between the house and the mirror is 25 feet
∴ HM = 25
- Paul and the house are both perpendicular to the ground
∴ TH and EP ⊥ HM at H and E
∴ TH // EP
- Paul's eyes are 6 feet above the ground
∴ EP = 6
- All these situations represent two triangles THM and EPM
- Δ THM represents the house , the tip of the roof and the mirror
- Δ EPM represents Paul's eyes , Paul position and the mirror
- In Δ THM
∵ TH // EP
∴ m∠ THM = m∠ EPM ⇒ alternate angles
∴ m∠ HTM = m∠ PEM ⇒ alternate angles
∴ Δ THM ≈ Δ EPM ⇒ AA similarity
∴ EP/TH = MP/MH
∵ EP = 6 , MP = 5 , MH = 25
∴ 6/TH = 5/25 ⇒ by using cross multiplication
∴ 5 TH = 6 × 25
∴ 5 TH = 150 ⇒ divide both sides by 5
∴ TH = 30
- TH is the height of the house
* The height of the house is 30 feet
